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

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1. 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
 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$spaces,, composition operator, compact operator, essential normCategories:47B38, 47B10, 46E40, 46E15 3. CMB 1999 (vol 42 pp. 97) Kwon, E. G.  On Analytic Functions of Bergman$\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
 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