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arXiv · 1703.06333

Sharp estimates for the gradient of the generalized Poisson integral for a half-space

Gershon Kresin·Vladimir Maz'ya
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Abstract

A representation of the sharp coefficient in a pointwise estimate for the gradient of the generalized Poisson integral of a function $f$ on ${\mathbb R}^n$ is obtained under the assumption that $f$ belongs to $L^p$. The explicit value of the coefficient is found for the cases $p=1$ and $p=2$.

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Gershon Kresin, Vladimir Maz'ya. 2017-03-18. Sharp estimates for the gradient of the generalized Poisson integral for a half-space. https://arxiv.org/abs/1703.06333

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