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

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1. CMB 2017 (vol 60 pp. 571)

Li, Ji; Wick, Brett D.
 Weak Factorizations of the Hardy space $H^1(\mathbb{R}^n)$ in terms of Multilinear Riesz Transforms This paper provides a constructive proof of the weak factorization of the classical Hardy space $H^1(\mathbb{R}^n)$ in terms of multilinear Riesz transforms. As a direct application, we obtain a new proof of the characterization of ${\rm BMO}(\mathbb{R}^n)$ (the dual of $H^1(\mathbb{R}^n)$) via commutators of the multilinear Riesz transforms. Keywords:Hardy space, BMO space, multilinear Riesz transform, weak factorizationCategories:42B35, 42B20

2. CMB 2015 (vol 59 pp. 197)

Rajaee, Saeed
 Quasi-copure Submodules All rings are commutative with identity and all modules are unital. In this paper we introduce the concept of quasi-copure submodule of a multiplication $R$-module $M$ and will give some results of them. We give some properties of tensor product of finitely generated faithful multiplication modules. Keywords:multiplication module, arithmetical ring, copure submodule, radical of submodulesCategories:13A15, 13C05, 13C13, , 13C99

3. CMB 2015 (vol 58 pp. 507)

Hsu, Ming-Hsiu; Lee, Ming-Yi
 VMO Space Associated with Parabolic Sections and its Application In this paper we define $VMO_\mathcal{P}$ space associated with a family $\mathcal{P}$ of parabolic sections and show that the dual of $VMO_\mathcal{P}$ is the Hardy space $H^1_\mathcal{P}$. As an application, we prove that almost everywhere convergence of a bounded sequence in $H^1_\mathcal{P}$ implies weak* convergence. Keywords:Monge-Ampere equation, parabolic section, Hardy space, BMO, VMOCategory:42B30

4. 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 submoduleCategories:13A99, 13C99, 13C13, 13E05

5. CMB 2012 (vol 56 pp. 466)

 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 surfaceCategories:30F35, 30H25, 30H30

6. 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 theoryCategory:16S90

7. 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 submodulesCategory:47B38

8. 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$spaces,, composition operator, compact operator, essential normCategories:47B38, 47B10, 46E40, 46E15 9. CMB 1999 (vol 42 pp. 463) Hofmann, Steve; Li, Xinwei; Yang, Dachun  A Generalized Characterization of Commutators of Parabolic Singular Integrals Let$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, symbolCategory:42B20 10. 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,$A_p$weightsCategory:42C10 11. 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 functionCategory:32A37

12. 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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