Journal of Operator Theory

Volume 72, Issue 1, Summer 2014 pp. 159-191.

Multipliers of Dirichlet subspaces of the Bloch space

Authors: Christos Chatzifountas (1), Daniel Girela (2), and Jose Angel Pelaez (3)
Author institution: (1) Departamento de Analisis Matematico, Universidad de Malaga, Campus de Teatinos, 29071 Malaga, Spain
(2) Departamento de Analisis Matematico, Universidad de Malaga, Campus de Teatinos, 29071 Malaga, Spain
(3) Departamento de Analisis Matematico, Universidad de Malaga, Campus de Teatinos, 29071 Malaga, Spain

Summary: For $0\lt p \lt \infty $ we let $\mathcal D^p_{p-1}$ be the space of all functions $f$ which are analytic in the unit disc $\mathbb{D}$ and satisfy $\int\limits_\mathbb{D} (1-\vert z\vert)^{p-1}\vert f'(z)\vert^ p \mathrm dA(z)<\infty $. It is known that, whenever $p\neq q$, the only multiplier from $\mathcal D^p_{p-1} $ to $\mathcal D^q_{q-1} $ is the trivial one. However, if $X$ is a subspace of the Bloch space and $0

DOI: http://dx.doi.org/10.7900/jot.2012nov20.1979
Keywords: Bloch space, BMOA, Hardy spaces, spaces of Dirichlet type, multipliers, lacunary power series, random power series

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