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Search: MSC category 46E15 ( Banach spaces of continuous, differentiable or analytic functions )

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1. CJM Online first

Bao, Guanlong; Göğüş, Nihat Gökhan; Pouliasis, Stamatis
 On Dirichlet spaces with a class of superharmonic weights In this paper, we investigate Dirichlet spaces $\mathcal{D}_\mu$ with superharmonic weights induced by positive Borel measures $\mu$ on the open unit disk. We establish the Alexander-Taylor-Ullman inequality for $\mathcal{D}_\mu$ spaces and we characterize the cases where equality occurs. We define a class of weighted Hardy spaces $H_{\mu}^{2}$ via the balayage of the measure $\mu$. We show that $\mathcal{D}_\mu$ is equal to $H_{\mu}^{2}$ if and only if $\mu$ is a Carleson measure for $\mathcal{D}_\mu$. As an application, we obtain the reproducing kernel of $\mathcal{D}_\mu$ when $\mu$ is an infinite sum of point mass measures. We consider the boundary behavior and inner-outer factorization of functions in $\mathcal{D}_\mu$. We also characterize the boundedness and compactness of composition operators on $\mathcal{D}_\mu$. Keywords:Dirichlet space, Hardy space, superharmonic weightCategories:30H10, 31C25, 46E15

2. CJM 2010 (vol 62 pp. 961)

Aleman, Alexandru; Duren, Peter; Martín, María J.; Vukotić, Dragan
 Multiplicative Isometries and Isometric Zero-Divisors For some Banach spaces of analytic functions in the unit disk (weighted Bergman spaces, Bloch space, Dirichlet-type spaces), the isometric pointwise multipliers are found to be unimodular constants. As a consequence, it is shown that none of those spaces have isometric zero-divisors. Isometric coefficient multipliers are also investigated. Keywords:Banach spaces of analytic functions, Hardy spaces, Bergman spaces, Bloch space, Dirichlet space, Dirichlet-type spaces, pointwise multipliers, coefficient multipliers, isometries, isometric zero-divisorsCategories:30H05, 46E15

3. CJM 2009 (vol 61 pp. 50)

Chen, Huaihui; Gauthier, Paul
 Composition operators on $\mu$-Bloch spaces Given a positive continuous function $\mu$ on the interval $0 Categories:47B33, 32A70, 46E15 4. CJM 2006 (vol 58 pp. 548) Galanopoulos, P.; Papadimitrakis, M.  Hausdorff and Quasi-Hausdorff Matrices on Spaces of Analytic Functions We consider Hausdorff and quasi-Hausdorff matrices as operators on classical spaces of analytic functions such as the Hardy and the Bergman spaces, the Dirichlet space, the Bloch spaces and$\BMOA$. When the generating sequence of the matrix is the moment sequence of a measure$\mu$, we find the conditions on$\mu$which are equivalent to the boundedness of the matrix on the various spaces. Categories:47B38, 46E15, 40G05, 42A20 5. CJM 1999 (vol 51 pp. 309) Leung, Denny H.; Tang, Wee-Kee  Symmetric sequence subspaces of$C(\alpha)$, II If$\alpha$is an ordinal, then the space of all ordinals less than or equal to$\alpha$is a compact Hausdorff space when endowed with the order topology. Let$C(\alpha)$be the space of all continuous real-valued functions defined on the ordinal interval$[0, \alpha]$. We characterize the symmetric sequence spaces which embed into$C(\alpha)$for some countable ordinal$\alpha$. A hierarchy$(E_\alpha)$of symmetric sequence spaces is constructed so that, for each countable ordinal$\alpha$,$E_\alpha$embeds into$C(\omega^{\omega^\alpha})$, but does not embed into$C(\omega^{\omega^\beta})$for any$\beta < \alpha$. Categories:03E13, 03E15, 46B03, 46B45, 46E15, 54G12 6. CJM 1997 (vol 49 pp. 100) Lance, T. L.; Stessin, M. I.  Multiplication Invariant Subspaces of Hardy Spaces This paper studies closed subspaces$L$of the Hardy spaces$H^p$which are$g$-invariant ({\it i.e.},$g\cdot L \subseteq L)$where$g$is inner,$g\neq 1$. If$p=2$, the Wold decomposition theorem implies that there is a countable $g$-basis''$f_1, f_2,\ldots$of$L$in the sense that$L$is a direct sum of spaces$f_j\cdot H^2[g]$where$H^2[g] = \{f\circ g \mid f\in H^2\}$. The basis elements$f_j$satisfy the additional property that$\int_T |f_j|^2 g^k=0$,$k=1,2,\ldots\,.$We call such functions$g$-$2$-inner. It also follows that any$f\in H^2$can be factored$f=h_{f,2}\cdot (F_2\circ g)$where$h_{f,2}$is$g$-$2$-inner and$F$is outer, generalizing the classical Riesz factorization. Using$L^p$estimates for the canonical decomposition of$H^2$, we find a factorization$f=h_{f,p} \cdot (F_p \circ g)$for$f\in H^p$. If$p\geq 1$and$g$is a finite Blaschke product we obtain, for any$g$-invariant$L\subseteq H^p$, a finite$g$-basis of$g$-$p\$-inner functions. Categories:30H05, 46E15, 47B38
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