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arXiv · 1411.2270

A Reproducing Kernel Thesis for Operators on $\ell^2$--valued Bergman-type Function Spaces

Robert Rahm
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Abstract

In this paper we consider the reproducing kernel thesis for boundedness and compactness for operators on $\ell^2$--valued Bergman-type spaces. This paper generalizes many well--known results about classical function spaces to their $\ell^2$--valued versions. In particular, the results in this paper apply to the weighted $\ell^2$--valued Bergman space on the unit ball, the unit polydisc and, more generally to weighted Fock spaces.

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Robert Rahm. 2014-11-09. A Reproducing Kernel Thesis for Operators on $\ell^2$--valued Bergman-type Function Spaces. https://doi.org/10.1007/s11785-015-0473-8

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