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arXiv · 1212.0737

Fock-Sobolev spaces and their Carleson measures

Hongrae Cho·Kehe Zhu
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Abstract

We consider the Fock-Sobolev space $F^{p,m}$ consisting of entire functions $f$ such that $f^{(m)}$, the $m$-th order derivative of $f$, is in the Fock space $F^p$. We show that an entire function $f$ is in $F^{p,m}$ if and only if the function $z^mf(z)$ is in $F^p$. We also characterize the Carleson measures for the spaces $F^{p,m}$, establish the boundedness of the weighted Fock projection on appropriate $L^p$ spaces, identify the Banach dual of $F^{p,m}$, and compute the complex interpolation space between two $F^{p,m}$ spaces.

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Hongrae Cho, Kehe Zhu. 2012-12-04. Fock-Sobolev spaces and their Carleson measures. https://arxiv.org/abs/1212.0737

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