Commutators for Approximation Spaces and Marcinkiewicz-Type Multipliers

Authors: Cerdà J.1; Martín J.2; Ditzian N.Z.Y.

Source: Journal of Approximation Theory, Volume 100, Number 2, October 1999 , pp. 251-265(15)

Publisher: Academic Press

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Abstract:

It is proved that, under some conditions, weaker than those of the Marcinkiewicz multiplier theorem, the multiplier operator Tmu(sumk ckeikt)=sumk mukckeikt satisfies on the Besov space Bsigma, qp the commutator theoremVerbar[T, Tmu]VerbarBsigma, qp, Bsigma, qplesc VerbarTVerbar,where VerbarTVerbar=max(VerbarTVerbarBsigma0, q0p, Bsigma0, q0p, VerbarTVerbarBsigma1, q1p, Bsigma1, q1p and sigma0>sigma>sigma1>0. Copyright 1999 Academic Press.

Language: English

Document Type: Research article

Affiliations: 1: Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Barcelona, E-08071, Spain 2: Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Barcelona, E-08071, Spain

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