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arXiv · 1801.06709

Vector valued Hardy spaces related to analytic functions having distributional boundary values

Richard D. Carmichael·Stevan Pilipović·Jasson Vindas
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Abstract

The Hardy space $H^{p}$ of vector valued analytic functions in tube domains in $\mathbb{C}^{n}$ and with values in Banach space are defined. Vector valued analytic functions in tube domains in $\mathbb{C}^{n}$ with values in Hilbert space and which have vector valued tempered distributions as boundary value are proved to be in $H^{p}$ corresponding to Hilbert space if the boundary value is in $L^{p}$ with values in Hilbert space. A Poisson integral representation for such vector valued analytic functions is obtained.

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Richard D. Carmichael, Stevan Pilipović, Jasson Vindas. 2018-01-20. Vector valued Hardy spaces related to analytic functions having distributional boundary values. https://doi.org/10.1080/17476933.2018.1545763

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