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Commutators for Approximation Spaces and Marcinkiewicz-Type Multipliers

Authors:	Joan Cerd Joaquim Martín Natan Ya Krugljak

Institution:	Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, E-08071, Barcelona, Spain^f1;Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, E-08071, Barcelona, Spain^,^f2;Department of Mathematics, Yaroslavl State University, Yaroslavl, Russia^,^f3

Abstract:	It is proved that, under some conditions, weaker than those of the Marcinkiewicz multiplier theorem, the multiplier operator T_μ(∑_k c_ke^ikt)=∑_k μ_kc_ke^ikt satisfies on the Besov space B^σ, q_p the commutator theoremT, T_μ]_{B^σ, q_p, B^σ, q_p}c T, where T=max(T_{B^σ₀, q₀_p, B^σ₀, q₀_p}, T_{B^σ₁, q₁_p, B^σ₁, q₁_p} and σ₀>σ>σ₁>0.

Keywords:	multipliers commutator K-functional approximation spaces Besov space
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