Expand all Collapse all | Results 1 - 25 of 43 |
1. CJM Online first
Non-tangential Maximal Function Characterizations of Hardy Spaces Associated with Degenerate Elliptic Operators |
Non-tangential Maximal Function Characterizations of Hardy Spaces Associated with Degenerate Elliptic Operators Let $w$ be either in the Muckenhoupt class of $A_2(\mathbb{R}^n)$ weights
or in the class of $QC(\mathbb{R}^n)$ weights, and
$L_w:=-w^{-1}\mathop{\mathrm{div}}(A\nabla)$
the degenerate elliptic operator on the Euclidean space $\mathbb{R}^n$,
$n\ge 2$. In this article, the authors establish the non-tangential
maximal function characterization
of the Hardy space $H_{L_w}^p(\mathbb{R}^n)$ associated with $L_w$ for
$p\in (0,1]$ and, when $p\in (\frac{n}{n+1},1]$ and
$w\in A_{q_0}(\mathbb{R}^n)$ with $q_0\in[1,\frac{p(n+1)}n)$,
the authors prove that the associated Riesz transform $\nabla L_w^{-1/2}$
is bounded from $H_{L_w}^p(\mathbb{R}^n)$ to the weighted classical
Hardy space $H_w^p(\mathbb{R}^n)$.
Keywords:degenerate elliptic operator, Hardy space, square function, maximal function, molecule, Riesz transform Categories:42B30, 42B35, 35J70 |
2. CJM Online first
Twisted Vertex Operators and Unitary Lie Algebras A representation of the central extension of the
unitary Lie algebra
coordinated with a skew Laurent polynomial ring
is constructed using vertex operators over an integral $\mathbb Z_2$-lattice.
The irreducible decomposition of the representation is explicitly computed and described.
As a by-product, some fundamental representations of affine
Kac-Moody Lie algebra of type $A_n^{(2)}$ are recovered
by the new method.
Keywords:Lie algebra, vertex operator, representation theory Categories:17B60, 17B69 |
3. CJM 2013 (vol 67 pp. 132)
Unitary Equivalence and Similarity to Jordan Models for Weak Contractions of Class $C_0$ We obtain results on the unitary equivalence of weak contractions of
class $C_0$ to their Jordan models under an assumption on their
commutants. In particular, our work addresses the case of arbitrary
finite multiplicity. The main tool is the
theory of boundary representations due to Arveson. We also
generalize and improve previously known results concerning unitary
equivalence and similarity to Jordan models when the minimal function
is a Blaschke product.
Keywords:weak contractions, operators of class $C_0$, Jordan model, unitary equivalence Categories:47A45, 47L55 |
4. CJM 2013 (vol 66 pp. 1382)
Weighted Carleson Measure Spaces Associated with Different Homogeneities In this paper, we introduce weighted Carleson measure spaces associated
with different homogeneities and prove that these spaces are the dual spaces
of weighted Hardy spaces studied in a forthcoming paper.
As an application, we establish
the boundedness of composition of two CalderÃ³n-Zygmund operators with
different homogeneities on the weighted Carleson measure spaces; this,
in particular, provides the weighted endpoint estimates for the operators
studied by Phong-Stein.
Keywords:composition of operators, weighted Carleson measure spaces, duality Categories:42B20, 42B35 |
5. CJM 2013 (vol 66 pp. 387)
Composition of Inner Functions We study the image of the model subspace $K_\theta$ under the
composition operator $C_\varphi$, where $\varphi$ and $\theta$ are
inner functions, and find the smallest model subspace which contains
the linear manifold $C_\varphi K_\theta$. Then we characterize the
case when $C_\varphi$ maps $K_\theta$ into itself. This case leads to
the study of the inner functions $\varphi$ and $\psi$ such that the
composition $\psi\circ\varphi$ is a divisor of $\psi$ in the family of
inner functions.
Keywords:composition operators, inner functions, Blaschke products, model subspaces Categories:30D55, 30D05, 47B33 |
6. CJM 2013 (vol 65 pp. 1217)
Beltrami Equation with Coefficient in Sobolev and Besov Spaces Our goal in this work is to present some function spaces on the
complex plane $\mathbb C$, $X(\mathbb C)$, for which the quasiregular solutions of
the Beltrami equation, $\overline\partial f (z) = \mu(z) \partial f
(z)$, have first derivatives locally in $X(\mathbb C)$, provided that the
Beltrami coefficient $\mu$ belongs to $X(\mathbb C)$.
Keywords:quasiregular mappings, Beltrami equation, Sobolev spaces, CalderÃ³n-Zygmund operators Categories:30C62, 35J99, 42B20 |
7. CJM 2012 (vol 65 pp. 989)
Automatic Continuity of Homomorphisms in Non-associative Banach Algebras We introduce the concept of a rare element in a non-associative normed
algebra and show that the existence of such element is the only obstruction
to continuity of a surjective homomorphism from a non-associative Banach
algebra to a unital normed algebra with simple completion. Unital
associative algebras do not admit any rare element and hence automatic
continuity holds.
Keywords:automatic continuity, non-associative algebra, spectrum, rare operator, rare element Categories:46H40, 46H70 |
8. CJM 2011 (vol 64 pp. 1036)
Harmonic Analysis Related to Homogeneous Varieties in Three Dimensional Vector Spaces over Finite Fields |
Harmonic Analysis Related to Homogeneous Varieties in Three Dimensional Vector Spaces over Finite Fields In this paper we study the extension problem, the
averaging problem, and the generalized ErdÅs-Falconer distance
problem associated with arbitrary homogeneous varieties in three
dimensional vector spaces over finite fields. In the case when the
varieties do not contain any plane passing through the origin, we
obtain the best possible results on the aforementioned three problems. In
particular, our result on the extension problem modestly generalizes
the result by Mockenhaupt and Tao who studied the particular conical
extension problem. In addition, investigating the Fourier decay on
homogeneous varieties enables us to give complete mapping properties
of averaging operators. Moreover, we improve the size condition on a
set such that the cardinality of its distance set is nontrivial.
Keywords:extension problems, averaging operator, finite fields, ErdÅs-Falconer distance problems, homogeneous polynomial Categories:42B05, 11T24, 52C17 |
9. CJM 2011 (vol 64 pp. 1329)
Composition Operators Induced by Analytic Maps to the Polydisk We study properties of composition operators
induced by symbols acting from the unit disk to the polydisk.
This result will be involved in the investigation
of weighted composition operators on the Hardy space on the unit disk
and moreover be concerned with composition operators acting
from the Bergman space to the Hardy space on the unit disk.
Keywords:composition operators, Hardy spaces, polydisk Categories:47B33, 32A35, 30H10 |
10. CJM 2011 (vol 64 pp. 669)
The Genuine Omega-regular Unitary Dual of the Metaplectic Group We classify all genuine unitary representations of the metaplectic group whose
infinitesimal character is real and at least as regular as that of the
oscillator representation. In a previous paper we exhibited a certain family
of representations satisfying these conditions, obtained by cohomological
induction from the tensor product of a one-dimensional representation and an
oscillator representation. Our main theorem asserts that this family exhausts
the genuine omega-regular unitary dual of the metaplectic group.
Keywords:Metaplectic group, oscillator representation, bottom layer map, cohomological induction, Parthasarathy's Dirac Operator Inequality, pseudospherical principal series Category:22E46 |
11. CJM 2011 (vol 64 pp. 805)
Quantum Random Walks and Minors of Hermitian Brownian Motion Considering quantum random walks, we construct discrete-time
approximations of the eigenvalues processes of minors of Hermitian
Brownian motion. It has been recently proved by Adler, Nordenstam, and
van Moerbeke that the process of eigenvalues of
two consecutive minors of a Hermitian Brownian motion is a Markov
process; whereas, if one considers more than two consecutive minors,
the Markov property fails. We show that there are analog results in
the noncommutative counterpart and establish the Markov property of
eigenvalues of some particular submatrices of Hermitian Brownian
motion.
Keywords:quantum random walk, quantum Markov chain, generalized casimir operators, Hermitian Brownian motion, diffusions, random matrices, minor process Categories:46L53, 60B20, 14L24 |
12. CJM 2011 (vol 64 pp. 892)
Boundedness of CalderÃ³n-Zygmund Operators on Non-homogeneous Metric Measure Spaces Let $({\mathcal X}, d, \mu)$ be a
separable metric measure space satisfying the known upper
doubling condition, the geometrical doubling condition, and the
non-atomic condition that $\mu(\{x\})=0$ for all $x\in{\mathcal X}$.
In this paper, we show that the boundedness of a CalderÃ³n-Zygmund
operator $T$ on $L^2(\mu)$ is equivalent to that of $T$ on
$L^p(\mu)$ for some $p\in (1, \infty)$, and that of $T$ from $L^1(\mu)$
to $L^{1,\,\infty}(\mu).$ As an application, we prove that if $T$ is a
CalderÃ³n-Zygmund operator bounded on $L^2(\mu)$,
then its maximal operator is bounded on $L^p(\mu)$
for all $p\in (1, \infty)$ and from
the space of all complex-valued Borel measures on
${\mathcal X}$ to $L^{1,\,\infty}(\mu)$.
All these results generalize the corresponding results of Nazarov et al.
on metric spaces with
measures satisfying the so-called polynomial growth condition.
Keywords:upper doubling, geometrical doubling, dominating function, weak type $(1,1)$ estimate, CalderÃ³n-Zygmund operator, maximal operator Categories:42B20, 42B25, 30L99 |
13. CJM 2011 (vol 64 pp. 183)
Negative Powers of Laguerre Operators We study negative powers of Laguerre differential operators in $\mathbb{R}^d$, $d\ge1$.
For these operators we prove two-weight $L^p-L^q$ estimates with ranges of $q$ depending
on $p$. The case of the harmonic oscillator (Hermite operator) has recently
been treated by Bongioanni and Torrea by using a straightforward
approach of kernel estimates. Here these results are applied in certain Laguerre settings.
The procedure is fairly direct for Laguerre function expansions of
Hermite type,
due to some monotonicity properties of the kernels involved.
The case of Laguerre function expansions of convolution type is less straightforward.
For half-integer type indices $\alpha$ we transfer the desired results from the Hermite setting
and then apply an interpolation argument based on a device we call the
Keywords:potential operator, fractional integral, Riesz potential, negative power, harmonic oscillator, Laguerre operator, Dunkl harmonic oscillator Categories:47G40, 31C15, 26A33 |
14. CJM 2011 (vol 63 pp. 862)
Linear Combinations of Composition Operators on the Bloch Spaces We characterize the compactness of linear combinations of analytic
composition operators on the Bloch space. We also study
their boundedness and compactness on the little Bloch space.
Keywords: composition operator, compactness, Bloch space Categories:47B33, 30D45, 47B07 |
15. CJM 2010 (vol 63 pp. 181)
Characterizations of Continuous and Discrete $q$-Ultraspherical Polynomials
We characterize the continuous $q$-ultraspherical polynomials in
terms of the special form of the coefficients in the expansion
$\mathcal{D}_q P_n(x)$ in the basis $\{P_n(x)\}$, $\mathcal{D}_q$
being the Askey--Wilson divided difference operator. The polynomials
are assumed to be symmetric, and the connection coefficients
are multiples of the reciprocal of the square of the $L^2$ norm of
the polynomials. A similar characterization is given for the discrete
$q$-ultraspherical polynomials. A new proof of the evaluation of
the connection coefficients for big $q$-Jacobi polynomials is given.
Keywords:continuous $q$-ultraspherical polynomials, big $q$-Jacobi polynomials, discrete $q$-ultra\-spherical polynomials, Askey--Wilson operator, $q$-difference operator, recursion coefficients Categories:33D45, 42C05 |
16. CJM 2010 (vol 62 pp. 1419)
BMO-Estimates for Maximal Operators via Approximations of the Identity with Non-Doubling Measures
Let $\mu$ be a nonnegative Radon measure
on $\mathbb{R}^d$ that satisfies the growth condition that there exist
constants $C_0>0$ and $n\in(0,d]$ such that for all $x\in\mathbb{R}^d$ and
$r>0$, ${\mu(B(x,\,r))\le C_0r^n}$, where $B(x,r)$ is the open ball
centered at $x$ and having radius $r$. In this paper, the authors prove
that if $f$ belongs to the $\textrm {BMO}$-type space $\textrm{RBMO}(\mu)$ of Tolsa, then
the homogeneous maximal function $\dot{\mathcal{M}}_S(f)$ (when $\mathbb{R}^d$ is not an
initial cube) and the inhomogeneous maximal function
$\mathcal{M}_S(f)$ (when $\mathbb{R}^d$ is an initial cube)
associated with a given approximation of the identity $S$ of Tolsa are
either infinite everywhere or finite almost everywhere,
and in the latter case, $\dot{\mathcal{M}}_S$ and $\mathcal{M}_S$ are bounded from
$\textrm{RBMO}(\mu)$ to the $\textrm {BLO}$-type
space $\textrm{RBLO}(\mu)$. The authors also prove that the inhomogeneous
maximal operator $\mathcal{M}_S$ is bounded from the local
$\textrm {BMO}$-type space $\textrm{rbmo}(\mu)$
to the local $\textrm {BLO}$-type space $\textrm{rblo}(\mu)$.
Keywords:Non-doubling measure, maximal operator, approximation of the identity, RBMO(mu), RBLO(mu), rbmo(mu), rblo(mu) Categories:42B25, 42B30, 47A30, 43A99 |
17. CJM 2010 (vol 62 pp. 1037)
Riemann Extensions of Torsion-Free Connections with Degenerate Ricci Tensor
{Correspondence} between torsion-free connections with {nilpotent skew-symmetric curvature operator} and IP Riemann
extensions is shown. Some consequences are derived in the study of
four-dimensional IP metrics and locally homogeneous affine surfaces.
Keywords:Walker metric, Riemann extension, curvature operator, projectively flat and recurrent affine connection Categories:53B30, 53C50 |
18. CJM 2009 (vol 62 pp. 202)
Interior $h^1$ Estimates for Parabolic Equations with $\operatorname{LMO}$ Coefficients In this paper we establish
\emph{a priori} $h^1$-estimates in a bounded domain for parabolic
equations with vanishing $\operatorname{LMO}$ coefficients.
Keywords:parabolic operator, Hardy space, parabolic, singular integrals and commutators Categories:35K20, 35B65, 35R05 |
19. CJM 2009 (vol 62 pp. 305)
Approximation and Similarity Classification of Stably Finitely Strongly Irreducible Decomposable Operators |
Approximation and Similarity Classification of Stably Finitely Strongly Irreducible Decomposable Operators Let $\mathcal H$ be a complex separable Hilbert space and ${\mathcal L}({\mathcal H})$ denote the collection of bounded linear operators on ${\mathcal H}$. In this paper, we show that for any operator $A\in{\mathcal L}({\mathcal H})$, there exists a stably finitely (SI) decomposable operator $A_\epsilon$, such that $\|A-A_{\epsilon}\|<\epsilon$ and ${\mathcal{\mathcal A}'(A_{\epsilon})}/\operatorname{rad} {{\mathcal A}'(A_{\epsilon})}$ is commutative, where $\operatorname{rad}{{\mathcal A}'(A_{\epsilon})}$ is the Jacobson radical of ${{\mathcal A}'(A_{\epsilon})}$. Moreover, we give a similarity classification of the stably finitely decomposable operators that generalizes the result on similarity classification of Cowen-Douglas operators given by C. L. Jiang.
Keywords:$K_{0}$-group, strongly irreducible decomposition, CowenâDouglas operators, commutant algebra, similarity classification Categories:47A05, 47A55, 46H20 |
20. CJM 2009 (vol 62 pp. 218)
The General Definition of the Complex Monge--AmpÃ¨re Operator on Compact KÃ¤hler Manifolds We introduce a wide subclass ${\mathcal F}(X,\omega)$ of
quasi-plurisubharmonic functions in a compact KÃ¤hler manifold, on
which the complex Monge-AmpÃ¨re operator is well defined and the
convergence theorem is valid. We also prove that ${\mathcal F}(X,\omega)$
is a convex cone and includes all quasi-plurisubharmonic functions
that are in the Cegrell class.
Keywords:complex Monge--AmpÃ¨re operator, compact KÃ¤hler manifold Categories:32W20, 32Q15 |
21. CJM 2009 (vol 61 pp. 1262)
On the Local Lifting Properties of Operator Spaces In this paper, we mainly study operator spaces which have the
locally lifting property (LLP). The dual of any ternary ring of operators is shown to
satisfy the strongly local reflexivity, and this is used to prove
that strongly local reflexivity holds also for operator spaces
which have the LLP. Several homological characterizations of the
LLP and weak expectation property are given. We also prove that for any operator space
$V$, $V^{**}$ has the LLP if and only if $V$ has the LLP and
$V^{*}$ is exact.
Keywords:operator space, locally lifting property, strongly locally reflexive Category:46L07 |
22. CJM 2009 (vol 61 pp. 190)
Bounded Hankel Products on the Bergman Space of the Polydisk We consider the problem of determining for which square integrable
functions $f$ and $g$ on the polydisk the densely defined Hankel
product $H_{f}H_g^\ast$ is bounded on the Bergman space of the
polydisk. Furthermore, we obtain similar results for the mixed
Haplitz products $H_{g}T_{\bar{f}}$ and $T_{f}H_{g}^{*}$, where $f$
and $g$ are square integrable on the polydisk and $f$ is analytic.
Keywords:Toeplitz operator, Hankel operator, Haplitz products, Bergman space, polydisk Categories:47B35, 47B47 |
23. CJM 2008 (vol 60 pp. 1010)
$H^\infty$ Functional Calculus and Mikhlin-Type Multiplier Conditions Let $T$ be a sectorial operator. It is known that the existence of a
bounded (suitably scaled) $H^\infty$ calculus for $T$, on every
sector containing the positive half-line, is equivalent to the
existence of a bounded functional calculus on the Besov algebra
$\Lambda_{\infty,1}^\alpha(\R^+)$. Such an algebra
includes functions defined by Mikhlin-type conditions and so the
Besov calculus can be seen as a result on multipliers for $T$. In
this paper, we use fractional derivation to analyse in detail the
relationship between $\Lambda_{\infty,1}^\alpha$ and Banach algebras
of Mikhlin-type. As a result, we obtain a new version of the quoted
equivalence.
Keywords:functional calculus, fractional calculus, Mikhlin multipliers, analytic semigroups, unbounded operators, quasimultipliers Categories:47A60, 47D03, 46J15, 26A33, 47L60, 47B48, 43A22 |
24. CJM 2008 (vol 60 pp. 241)
Semi-Classical Wavefront Set and Fourier Integral Operators Here we define and prove some properties of the semi-classical
wavefront set. We also define and study semi-classical Fourier
integral operators and prove a generalization of Egorov's theorem to
manifolds of different dimensions.
Keywords:wavefront set, Fourier integral operators, Egorov theorem, semi-classical analysis Categories:35S30, 35A27, 58J40, 81Q20 |
25. CJM 2007 (vol 59 pp. 1223)
CalderÃ³n--Zygmund Operators Associated to Ultraspherical Expansions We define the higher order Riesz transforms and the Littlewood--Paley
$g$-function
associated to the differential operator $L_\l f(\theta)=-f''(\theta)-2\l\cot\theta
f'(\theta)+\l^2f(\theta)$. We prove that these operators are
Calder\'{o}n--Zygmund operators in the homogeneous type space
$((0,\pi),(\sin t)^{2\l}\,dt)$. Consequently, $L^p$ weighted,
$H^1-L^1$ and $L^\infty-BMO$ inequalities are obtained.
Keywords:ultraspherical polynomials, CalderÃ³n--Zygmund operators Categories:42C05, 42C15frcs |