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

Gershon Kresin; Vladimir Maz'Ya

doi:10.1515/gmj-2018-0026

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

Gershon Kresin, Vladimir Maz'Ya

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	283-290
Number of pages	8
Journal	Georgian Mathematical Journal
Volume	25
Issue number	2
DOIs	https://doi.org/10.1515/gmj-2018-0026
State	Published - 1 Jun 2018

Keywords

Generalized Poisson integral
half-space
sharp estimate for the gradient

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10.1515/gmj-2018-0026

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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 ℝn is obtained under the assumption that f belongs to L p Lp . The explicit value of the coefficient is found for the cases p = 1 {p=1} and p = 2 p=2} .",

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

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