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Search: All articles in the CMB digital archive with keyword BMO

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1. CMB 2012 (vol 56 pp. 683)

Nikseresht, A.; Azizi, A.
Envelope Dimension of Modules and the Simplified Radical Formula
We introduce and investigate the notion of envelope dimension of commutative rings and modules over them. In particular, we show that the envelope dimension of a ring, $R$, is equal to that of the $R$-module $R^{(\mathbb{N})}$. Also we prove that the Krull dimension of a ring is no more than its envelope dimension and characterize Noetherian rings for which these two dimensions are equal. Moreover we generalize and study the concept of simplified radical formula for modules, which we defined in an earlier paper.

Keywords:envelope dimension, simplified radical formula, prime submodule
Categories:13A99, 13C99, 13C13, 13E05

2. CMB 2012 (vol 56 pp. 466)

Aulaskari, Rauno; Rättyä, Jouni
Inclusion Relations for New Function Spaces on Riemann Surfaces
We introduce and study some new function spaces on Riemann surfaces. For certain parameter values these spaces coincide with the classical Dirichlet space, BMOA or the recently defined $Q_p$ space. We establish inclusion relations that generalize earlier known inclusions between the above-mentioned spaces.

Keywords:Bloch space, BMOA, $Q_p$, Green's function, hyperbolic Riemann surface
Categories:30F35, 30H25, 30H30

3. CMB 2009 (vol 53 pp. 230)

Doğruöz, S.; Harmanci, A.; Smith, P. F.
Modules with Unique Closure Relative to a Torsion Theory
We consider when a single submodule and also when every submodule of a module M over a general ring R has a unique closure with respect to a hereditary torsion theory on $\operatorname{Mod}$-R.

Keywords:closed submodule, $UC$-module, torsion theory
Category:16S90

4. CMB 2004 (vol 47 pp. 456)

Seto, Michio
On the Berger-Coburn-Lebow Problem for Hardy Submodules
In this paper we shall give an affirmative solution to a problem, posed by Berger, Coburn and Lebow, for $C^{\ast}$-algebras on Hardy submodules.

Keywords:Hardy submodules
Category:47B38

5. CMB 2004 (vol 47 pp. 49)

Lindström, Mikael; Makhmutov, Shamil; Taskinen, Jari
The Essential Norm of a Bloch-to-$Q_p$ Composition Operator
The $Q_p$ spaces coincide with the Bloch space for $p>1$ and are subspaces of $\BMOA$ for $0
Keywords:Bloch space, little Bloch space, $\BMOA$, $\VMOA$, $Q_p$ spaces,, composition operator, compact operator, essential norm
Categories:47B38, 47B10, 46E40, 46E15

6. CMB 1999 (vol 42 pp. 463)

Hofmann, Steve; Li, Xinwei; Yang, Dachun
A Generalized Characterization of Commutators of Parabolic Singular Integrals
Let $x=(x_1, \dots, x_n)\in\rz$ and $\dz_\lz x=(\lz^{\az_1}x_1, \dots,\lz^{\az_n}x_n)$, where $\lz>0$ and $1\le \az_1\le\cdots \le\az_n$. Denote $|\az|=\az_1+\cdots+\az_n$. We characterize those functions $A(x)$ for which the parabolic Calder\'on commutator $$ T_{A}f(x)\equiv \pv \int_{\mathbb{R}^n} K(x-y)[A(x)-A(y)]f(y)\,dy $$ is bounded on $L^2(\mathbb{R}^n)$, where $K(\dz_\lz x)=\lz^{-|\az|-1}K(x)$, $K$ is smooth away from the origin and satisfies a certain cancellation property.

Keywords:parabolic singular integral, commutator, parabolic $\BMO$ sobolev space, homogeneous space, T1-theorem, symbol
Category:42B20

7. CMB 1999 (vol 42 pp. 198)

Guadalupe, José J.; Pérez, Mario; Varona, Juan L.
Commutators and Analytic Dependence of Fourier-Bessel Series on $(0,\infty)$
In this paper we study the boundedness of the commutators $[b, S_n]$ where $b$ is a $\BMO$ function and $S_n$ denotes the $n$-th partial sum of the Fourier-Bessel series on $(0,\infty)$. Perturbing the measure by $\exp(2b)$ we obtain that certain operators related to $S_n$ depend analytically on the functional parameter $b$.

Keywords:Fourier-Bessel series, commutators, BMO, $A_p$ weights
Category:42C10

8. CMB 1999 (vol 42 pp. 97)

Kwon, E. G.
On Analytic Functions of Bergman $\BMO$ in the Ball
Let $B = B_n$ be the open unit ball of $\bbd C^n$ with volume measure $\nu$, $U = B_1$ and ${\cal B}$ be the Bloch space on $U$. ${\cal A}^{2, \alpha} (B)$, $1 \leq \alpha < \infty$, is defined as the set of holomorphic $f\colon B \rightarrow \bbd C$ for which $$ \int_B \vert f(z) \vert^2 \left( \frac 1{\vert z\vert} \log \frac 1{1 - \vert z\vert } \right)^{-\alpha} \frac {d\nu (z)}{1-\vert z\vert} < \infty $$ if $0 < \alpha <\infty$ and ${\cal A}^{2, 1} (B) = H^2(B)$, the Hardy space. Our objective of this note is to characterize, in terms of the Bergman distance, those holomorphic $f\colon B \rightarrow U$ for which the composition operator $C_f \colon {\cal B} \rightarrow {\cal A}^{2, \alpha}(B)$ defined by $C_f (g) = g\circ f$, $g \in {\cal B}$, is bounded. Our result has a corollary that characterize the set of analytic functions of bounded mean oscillation with respect to the Bergman metric.

Keywords:Bergman distance, \BMOA$, Hardy space, Bloch function
Category:32A37

9. CMB 1997 (vol 40 pp. 475)

Lou, Zengjian
Coefficient multipliers of Bergman spaces $A^p$, II
We show that the multiplier space $(A^1,X)=\{g:M_\infty(r,g'') =O(1-r)^{-1}\}$, where $X$ is $\BMOA$, $\VMOA$, $B$, $B_0$ or disk algebra $A$. We give the multipliers from $A^1$ to $A^q(H^q)(1\le q\le \infty)$, we also give the multipliers from $l^p(1\le p\le 2), C_0, \BMOA$, and $H^p(2\le p<\infty)$ into $A^q(1\le q\le 2)$.

Keywords:Multiplier, Bergman space, Hardy space, Bloch space, $\BMOA$.
Categories:30H05, 30B10

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