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

2017/03/18 by Kresin, Gershon, Maz'ya, Vladimir
#Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 31B10 #Secondary: 31C99

paper · doi:10.48550/arxiv.1703.06333

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 Rⁿ 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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