We study the maximal function Mf(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 Bαp,q(RN) or in the Triebel‐Lizorkin space Fαp,q(RN). In particular, we prove that when Ω= {|y|N/ (N‐αp) < t < 1} the operator M is bounded from F αp,∞ (RN) into Lp (RN). The admissible regions for the spaces B αp,q (RN) with p < q are more complicated

Colzani, L., Laeng, E. (1995). Tangential Convergence of Temperatures and Harmonic Functions in Besov and in Triebel‐Lizorkin Spaces. MATHEMATISCHE NACHRICHTEN, 172(1), 65-86 [10.1002/mana.19951720106].

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

COLZANI, LEONARDO;
1995

Abstract

We study the maximal function Mf(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 Bαp,q(RN) or in the Triebel‐Lizorkin space Fαp,q(RN). In particular, we prove that when Ω= {|y|N/ (N‐αp) < t < 1} the operator M is bounded from F αp,∞ (RN) into Lp (RN). The admissible regions for the spaces B αp,q (RN) with p < q are more complicated
Articolo in rivista - Articolo scientifico
Tangential convergence; maximal function; Triebel-Lizorkin spaces; tangential maximal operators; Besov spaces
English
1995
172
1
65
86
none
Colzani, L., Laeng, E. (1995). Tangential Convergence of Temperatures and Harmonic Functions in Besov and in Triebel‐Lizorkin Spaces. MATHEMATISCHE NACHRICHTEN, 172(1), 65-86 [10.1002/mana.19951720106].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/19376
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