Homeomorphic changes of variable and Fourier multipliers

Abstract

We consider the algebras M p of Fourier multipliers and show that for every bounded continuous function f onMoreover, under certain assumptions on a family K of continuous functions, one h will suffice for all f ∈ K. A similar result holds for functions on the torus T d . This may be contrasted with the known solution of Luzin's problem related to the Wiener algebra.