Fourier multiplier theorems for Besov and Triebel-Lizorkin spaces with variable exponents

Abstract

In this paper, we will prove Fourier multiplier theorems on Besov and Triebel–Lizorkin spaces with variable exponents. It was shown by many authors that variable Triebel–Lizorkin spaces coincide with variable Bessel potential spaces, variable Sobolev spaces and variable Lebesgue spaces when appropriate indices are chosen. In consequence of the results, we also have Fourier multiplier theorems on these variable function spaces. Mathematics subject classification (2010): 42B15.