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26. CJM 2007 (vol 59 pp. 276)
Weighted Inequalities for HardySteklov Operators We characterize the pairs of weights $(v,w)$ for which the
operator $Tf(x)=g(x)\int_{s(x)}^{h(x)}f$ with $s$ and $h$
increasing and continuous functions is of strong type
$(p,q)$ or weak type $(p,q)$ with respect to the pair
$(v,w)$ in the case $0

27. CJM 2006 (vol 58 pp. 1121)
The Feichtinger Conjecture for Wavelet Frames, Gabor Frames and Frames of Translates The Feichtinger conjecture is considered for three special families of
frames. It is shown that if a wavelet frame satisfies a certain weak
regularity condition, then it can be written as the finite union of
Riesz basic sequences each of which is a wavelet system. Moreover, the
above is not true for general wavelet frames. It is also shown that a
supadjoint Gabor frame can be written as the finite union of Riesz
basic sequences. Finally, we show how existing techniques can be
applied to determine whether frames of translates can be written as
the finite union of Riesz basic sequences. We end by giving an example
of a frame of translates such that any Riesz basic subsequence must
consist of highly irregular translates.
Keywords:frame, Riesz basic sequence, wavelet, Gabor system, frame of translates, paving conjecture Categories:42B25, 42B35, 42C40 
28. CJM 2006 (vol 58 pp. 548)
Hausdorff and QuasiHausdorff Matrices on Spaces of Analytic Functions We consider Hausdorff and quasiHausdorff matrices as operators
on classical spaces of analytic functions such as the Hardy and
the Bergman spaces, the Dirichlet space, the Bloch spaces and $\BMOA$. When the generating
sequence of the matrix is the moment sequence of a measure $\mu$,
we find the conditions on $\mu$ which are equivalent to the boundedness
of the matrix on the various spaces.
Categories:47B38, 46E15, 40G05, 42A20 
29. CJM 2006 (vol 58 pp. 401)
On Pointwise Estimates of Positive Definite Functions With Given Support The following problem has been suggested by Paul Tur\' an. Let
$\Omega$ be a symmetric convex body in the Euclidean space $\mathbb R^d$
or in the torus $\TT^d$. Then, what is the largest possible value
of the integral of positive definite functions that are supported
in $\Omega$ and normalized with the value $1$ at the origin? From
this, Arestov, Berdysheva and Berens arrived at the analogous
pointwise extremal problem for intervals in $\RR$. That is, under
the same conditions and normalizations, the supremum of possible
function values at $z$ is to be found for any given point
$z\in\Omega$. However, it turns out that the problem for the real
line has already been solved by Boas and Kac, who gave several
proofs and also mentioned possible extensions to $\RR^d$ and to
nonconvex domains as well.
Here we present another approach to the problem, giving the
solution in $\RR^d$ and for several cases in~$\TT^d$. Actually, we
elaborate on the fact that the problem is essentially
onedimensional and investigate nonconvex open domains as well.
We show that the extremal problems are equivalent to some more
familiar ones concerning trigonometric polynomials, and thus find
the extremal values for a few cases. An analysis of the
relationship between the problem for $\RR^d$ and that for $\TT^d$
is given, showing that the former case is just the limiting case
of the latter. Thus the hierarchy of difficulty is established, so
that extremal problems for trigonometric polynomials gain renewed
recognition.
Keywords:Fourier transform, positive definite functions and measures, TurÃ¡n's extremal problem, convex symmetric domains, positive trigonometric polynomials, dual extremal problems Categories:42B10, 26D15, 42A82, 42A05 
30. CJM 2006 (vol 58 pp. 154)
Singular Integrals on Product Spaces Related to the Carleson Operator We prove $L^p(\mathbb T^2)$ boundedness, $1

31. CJM 2004 (vol 56 pp. 655)
On the Neumann Problem for the SchrÃ¶dinger Equations with Singular Potentials in Lipschitz Domains We consider the Neumann problem for the Schr\"odinger equations $\Delta u+Vu=0$,
with singular nonnegative potentials $V$ belonging to the reverse H\"older class
$\B_n$, in a connected Lipschitz domain $\Omega\subset\mathbf{R}^n$. Given
boundary data $g$ in $H^p$ or $L^p$ for $1\epsilon

32. CJM 2004 (vol 56 pp. 431)
Group Actions and Singular Martingales II, The Recognition Problem We continue our investigation in [RST] of a martingale formed by picking a
measurable set $A$ in a compact group $G$, taking random rotates of $A$, and
considering measures of the resulting intersections, suitably normalized. Here
we concentrate on the inverse problem of recognizing $A$ from a small amount of
data from this martingale. This leads to problems in harmonic analysis on $G$,
including an analysis of integrals of products of Gegenbauer polynomials.
Categories:43A77, 60B15, 60G42, 42C10 
33. CJM 2003 (vol 55 pp. 1134)
Norms of Complex Harmonic Projection Operators In this paper we estimate the $(L^pL^2)$norm of the complex
harmonic projectors $\pi_{\ell\ell'}$, $1\le p\le 2$, uniformly
with respect to the indexes $\ell,\ell'$. We provide sharp
estimates both for the projectors $\pi_{\ell\ell'}$, when
$\ell,\ell'$ belong to a proper angular sector in $\mathbb{N}
\times \mathbb{N}$, and for the projectors $\pi_{\ell 0}$ and
$\pi_{0 \ell}$. The proof is based on an extension of a complex
interpolation argument by C.~Sogge. In the appendix, we prove in a
direct way the uniform boundedness of a particular zonal kernel in
the $L^1$ norm on the unit sphere of $\mathbb{R}^{2n}$.
Categories:43A85, 33C55, 42B15 
34. CJM 2003 (vol 55 pp. 1019)
More Eventual Positivity for Analytic Functions Eventual positivity problems for real convergent Maclaurin series lead
to density questions for sets of harmonic functions. These are solved
for large classes of series, and in so doing, asymptotic estimates are
obtained for the values of the series near the radius of convergence
and for the coefficients of convolution powers.
Categories:30B10, 30D15, 30C50, 13A99, 41A58, 42A16 
35. CJM 2003 (vol 55 pp. 576)
Automorphic Orthogonal and Extremal Polynomials It is well known that many polynomials which solve extremal problems
on a single interval as the Chebyshev or the BernsteinSzeg\"o
polynomials can be represented by trigonometric functions and their
inverses. On two intervals one has elliptic instead of trigonometric
functions. In this paper we show that the counterparts of the Chebyshev
and BernsteinSzeg\"o polynomials for several intervals can be represented
with the help of automorphic functions, socalled SchottkyBurnside
functions. Based on this representation and using the SchottkyBurnside
automorphic functions as a tool several extremal properties of such
polynomials as orthogonality properties, extremal properties with
respect to the maximum norm, behaviour of zeros and recurrence
coefficients {\it etc.} are derived.
Categories:42C05, 30F35, 31A15, 41A21, 41A50 
36. CJM 2003 (vol 55 pp. 504)
Certain Operators with Rough Singular Kernels We study the singular integral operator
$$
T_{\Omega,\alpha}f(x) = \pv \int_{R^n} b(y) \Omega(y')
y^{n\alpha} f(xy)\,dy,
$$
defined on all test functions $f$,where $b$ is a bounded function, $\alpha\geq 0$,
$\Omega(y')$ is an integrable function on the unit sphere $S^{n1}$ satisfying
certain cancellation conditions. We prove that, for $1

37. CJM 2002 (vol 54 pp. 1165)
Multipliers on Vector Valued Bergman Spaces Let $X$ be a complex Banach space and let $B_p(X)$ denote the
vectorvalued Bergman space on the unit disc for $1\le p<\infty$. A
sequence $(T_n)_n$ of bounded operators between two Banach spaces $X$
and $Y$ defines a multiplier between $B_p(X)$ and $B_q(Y)$
(resp.\ $B_p(X)$ and $\ell_q(Y)$) if for any function $f(z) =
\sum_{n=0}^\infty x_n z^n$ in $B_p(X)$ we have that $g(z) =
\sum_{n=0}^\infty T_n (x_n) z^n$ belongs to $B_q(Y)$ (resp.\
$\bigl( T_n (x_n) \bigr)_n \in \ell_q(Y)$). Several results on these
multipliers are obtained, some of them depending upon the Fourier or
Rademacher type of the spaces $X$ and $Y$. New properties defined by
the vectorvalued version of certain inequalities for Taylor
coefficients of functions in $B_p(X)$ are introduced.
Categories:42A45, 46E40 
38. CJM 2002 (vol 54 pp. 634)
Frames and Single Wavelets for Unitary Groups We consider a unitary representation of a discrete countable abelian
group on a separable Hilbert space which is associated to a cyclic
generalized frame multiresolution analysis. We extend Robertson's
theorem to apply to frames generated by the action of the group.
Within this setup we use Stone's theorem and the theory of projection
valued measures to analyze wandering frame collections. This yields a
functional analytic method of constructing a wavelet from a
generalized frame multi\resolution analysis in terms of the frame
scaling vectors. We then explicitly apply our results to the action
of the integers given by translations on $L^2({\mathbb R})$.
Keywords:wavelet, multiresolution analysis, unitary group representation, frame Categories:42C40, 43A25, 42C15, 46N99 
39. CJM 2001 (vol 53 pp. 1031)
The Complete $(L^p,L^p)$ Mapping Properties of Some Oscillatory Integrals in Several Dimensions We prove that the operators $\int_{\mathbb{R}_+^2} e^{ix^a \cdot
y^b} \varphi (x,y) f(y)\, dy$ map $L^p(\mathbb{R}^2)$ into itself
for $p \in J =\bigl[\frac{a_l+b_l}{a_l+(\frac{b_l r}{2})},\frac{a_l+b_l}
{a_l(1\frac{r}{2})}\bigr]$ if $a_l,b_l\ge 1$ and $\varphi(x,y)=xy^{r}$,
$0\le r <2$, the result is sharp. Generalizations to dimensions $d>2$
are indicated.
Categories:42B20, 46B70, 47G10 
40. CJM 2001 (vol 53 pp. 565)
Spaces of Lorentz Multipliers We study when the spaces of Lorentz multipliers from $L^{p,t}
\rightarrow L^{p,s}$ are distinct. Our main interest is the case when
$s Keywords:multipliers, convolution operators, Lorentz spaces, Lorentzimproving multipliers Categories:43A22, 42A45, 46E30 
41. CJM 2000 (vol 52 pp. 381)
Hardy Space Estimate for the Product of Singular Integrals $H^p$ estimate for the multilinear operators which are finite sums
of pointwise products of singular integrals and fractional
integrals is given. An application to Sobolev space and some
examples are also given.
Keywords:$H^p$ space, multilinear operator, singular integral, fractional integration, Sobolev space Category:42B20 
42. CJM 2000 (vol 52 pp. 3)
On Small Complete Sets of Functions Using Local Residues and the Duality Principle a multidimensional
variation of the completeness theorems by T.~Carleman and A.~F.~Leontiev
is proven for the space of holomorphic functions defined on a suitable
open strip $T_{\alpha}\subset {\bf C}^2$. The completeness theorem is a
direct consequence of the Cauchy Residue Theorem in a torus. With
suitable modifications the same result holds in ${\bf C}^n$.
Categories:32A10, 42C30 
43. CJM 1998 (vol 50 pp. 1236)
The behaviour of Legendre and ultraspherical polynomials in $L_p$spaces We consider the analogue of the $\Lambda(p)$problem for
subsets of the Legendre polynomials or more general ultraspherical
polynomials. We obtain the ``best possible'' result that if $2

44. CJM 1998 (vol 50 pp. 1273)
Mean convergence of Lagrange interpolation for exponential weights on $[1,1]$ We obtain necessary and sufficient conditions for mean convergence of
Lagrange interpolation at zeros of orthogonal polynomials for weights on
$[1,1]$, such as
\[
w(x)=\exp \bigl((1x^{2})^{\alpha }\bigr),\quad \alpha >0
\]
or
\[
w(x)=\exp \bigl(\exp _{k}(1x^{2})^{\alpha }\bigr),\quad k\geq 1,
\ \alpha >0,
\]
where $\exp_{k}=\exp \Bigl(\exp \bigl(\cdots\exp (\ )\cdots\bigr)\Bigr)$
denotes the $k$th iterated exponential.
Categories:41A05, 42C99 
45. CJM 1998 (vol 50 pp. 605)
Hardy spaces of conjugate systems of temperatures We define Hardy spaces of conjugate systems of temperature functions on
${\bbd R}_{+}^{n+1}$. We show that their boundary distributions are the same
as the boundary distributions of the usual Hardy spaces of conjugate systems
of harmonic functions.
Categories:42B30, 42A50, 35K05 
46. CJM 1998 (vol 50 pp. 29)
Weighted norm inequalities for fractional integral operators with rough kernel Given function $\Omega$ on ${\Bbb R^n}$, we define the fractional
maximal operator and the fractional integral operator by
$$
M_{\Omega,\alpha}\,f(x)=\sup_{r>0}\frac 1{r^{n\alpha}}
\int_{\,y
Categories:42B20, 42B25 
47. CJM 1997 (vol 49 pp. 1010)
A characterization of two weight norm inequalities for onesided operators of fractional type In this paper we give a characterization of the pairs
of weights $(\w,v)$ such that $T$ maps $L^p(v)$ into
$L^q(\w)$, where $T$ is a general onesided operator
that includes as a particular case the Weyl fractional
integral. As an application we solve the following problem:
given a weight $v$, when is there a nontrivial weight
$\w$ such that $T$ maps $L^p(v)$ into $L^q(\w )$?
Keywords:Weyl fractional integral, weights Categories:26A33, 42B25 
48. CJM 1997 (vol 49 pp. 708)
Density questions for the truncated matrix moment problem For a truncated matrix moment problem, we describe in detail
the set of positive definite matrices of measures $\mu$ in $V_{2n}$ (this is
the set of solutions of the problem of degree $2n$) for which the polynomials
up to degree $n$ are dense in the corresponding space ${\cal L}^2(\mu)$.
These matrices of measures are exactly the extremal measures of the set $V_n$.
Categories:42C05, 44A60 
49. CJM 1997 (vol 49 pp. 175)
Orthogonal Polynomials for a Family of Product Weight Functions on the Spheres Based on the theory of spherical harmonics for measures invariant
under a finite reflection group developed by Dunkl recently, we study
orthogonal polynomials with respect to the weight functions
$x_1^{\alpha_1}\cdots x_d^{\alpha_d}$ on the unit sphere $S^{d1}$ in
$\RR^d$. The results include explicit formulae for orthonormal polynomials,
reproducing and Poisson kernel, as well as intertwining operator.
Keywords:Orthogonal polynomials in several variables, sphere, hharmonics Categories:33C50, 33C45, 42C10 