Pointwise multipliers for Triebel–Lizorkin and Besov spaces on Lie groups

Commutators for Fourier multipliers on Besov Spaces

The mapping properties of commutators [T,M ] = TM −MT , for operators between function spaces, and their various generalizations play an important role in harmonic analysis, PDE, interpolation theory and other related areas. A typical situation arises when M = Mb is the pointwise multiplication by a function b and T is a Calderón–Zygmund operator on R. Then well– known results of A.P. Calderón ...

Pointwise Multipliers of Besov Spaces of Smoothness Zero and Spaces of Continuous Functions

On the pointwise multiplication in Besov and Lizorkin-Triebel spaces

where F and B, with three indices, will denote the Lizorkin-Triebel space Fs p,q and the Besov space Bp,q, respectively. The different embeddings obtained here are under certain restrictions on the parameters. In this introduction, we will recall the definition of some spaces and some necessary tools. In Sections 2 and 3, we give the first contribution of this work. The theorems of Section 2 wi...

General Hörmander and Mikhlin Conditions for Multipliers of Besov Spaces

Abstract. Here a new condition for the geometry of Banach spaces is introduced and the operator–valued Fourier multiplier theorems in weighted Besov spaces are obtained. Particularly, connections between the geometry of Banach spaces and Hörmander-Mikhlin conditions are established. As an application of main results the regularity properties of degenerate elliptic differential operator equation...

Smooth pointwise multipliers of modulation spaces

Let 1 < p, q < ∞ and s, r ∈ R. It is proved that any function in the amalgam space W (H p′(R ), l∞), where p ′ is the conjugate exponent to p and H p′(R ) is the Bessel potential space, defines a bounded pointwise multiplication operator in the modulation space M p,q(R ), whenever r > |s|+ d.