On embedding properties of some extrapolation spaces
Martín i Pedret, Joaquim (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)
Carro, María J. (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)

Imprint:	New York : De Gruyter, 2002
Description:	8 pàg.
Abstract:	Given a sublinear operator T satisfying that ‖Tf‖Lp(ν) ≤ Cp−1‖f‖Lp(μ), for every 1 < p ≤ p0, with C independent of f and p, it has been recently proved that T : LlogL → M(φ), where M(φ) is the maximal Lorentz space with φ(t) = t(1 + log + t)−1. Also, if T satisfies that ‖Tf‖Lp(ν) ≤ Cp‖f‖Lp(μ), for every p ≥ p0, then T : Λ1(min(t − 1,1))∩L∞ → M(φ), where φ(t) =(1 + log + (1/t))−1. The purpose of this note, is to study embedding properties of the extrapolation spaces Llog L and M(φ) with respect toL1, and also embedding properties of Λ1(min(t − 1,1))∩L∞ and M(φ) with respect toL∞. We shall also extend these type of results to more general extrapolation theorems.
Grants:	Ministerio de Ciencia y Tecnología PB97-0986 Agència de Gestió d'Ajuts Universitaris i de Recerca 1999/SGR-00061
Rights:	Tots els drets reservats.
Language:	Anglès
Series:	De Gruyter Proceedings in Mathematics
Document:	Capítol de llibre ; Versió acceptada per publicar
Subject:	Real interpolation ; Extrapolation ; Maximal and minimal Lorentz spaces
Published in:	Function spaces, interpolation theory and related topics: Proceedings of the International Conference in honour of Jaak Peetre on his 65th birthday, 2002, p. 241-248

DOI: 10.1515/9783110198058.241

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