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Tangential Convergence of Temperatures and Harmonic Functions in Besov and in Triebel-Lizorkin Spaces

✍ Scribed by Leonardo Colzani; Enrico Laeng

Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
754 KB
Volume
172
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We study the maximal function M__f__(x) = sup |f(x + y, t)| when Ω is a region in the (y,t) Ω upper half space R and f(x, t) is the harmonic extension to R~+~^N+1^ of a distribution in the Besov space B^α^~p,q~(R__^N^) or in the Triebel‐Lizorkin space F^α^~p,q~(R^N^). In particular, we prove that when Ω= {|~y~|^N/ (N‐αp)^ < t < 1} the operator M is bounded from F (R^N^) into L^p^__ (R__^N^). The admissible regions for the spaces B (R^N^__) with p < q are more complicated.

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