Littlewood-Paley equivalence and homogeneous Fourier multipliers

Abstract

We consider certain Littlewood-Paley operators and prove characterization of some function spaces in terms of those operators. When treating weighted Lebesgue spaces, a generalization to weighted spaces will be made for Hörmander's theorem on the invertibility of homogeneous Fourier multipliers. Also, applications to the theory of Sobolev spaces will be given.

arXiv comment27 pages

References in corpus (2)

• Multiparameter Marcinkiewicz integrals and a resonance theorem
• A Marcinkiewicz integral type characterization of the Sobolev space

Cited by in corpus (1)

• Vector valued inequalities and Littlewood-Paley operators on Hardy spaces