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Tangential Convergence of Temperatures and Harmonic Functions in Besov and in Triebel‐Lizorkin Spaces
Author(s) -
Colzani Leonardo,
Laeng Enrico
Publication year - 1995
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19951720106
Subject(s) - mathematics , besov space , bounded function , space (punctuation) , operator (biology) , function space , harmonic function , extension (predicate logic) , function (biology) , mathematical analysis , combinatorics , distribution (mathematics) , convergence (economics) , pure mathematics , interpolation space , functional analysis , biochemistry , chemistry , linguistics , philosophy , repressor , evolutionary biology , biology , computer science , transcription factor , economics , gene , programming language , economic growth
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 N+1 +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 α p,∞(R N ) into L p (R N ). The admissible regions for the spaces B α p,q(R N ) with p < q are more complicated.