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Working paper

Homeomorphic Changes of Variable and Fourier Multipliers

arxiv.org. math. Cornell University, 2018. No. arXiv:1803.02177v1.
V. Lebedev, Olevskii A.
We consider the algebras M_p of Fourier multipliers and show that every bounded continuous function f on  R^d can be transformed by an appropriate homeomorphic change of variable into a function that belongs to M_p(R^d) for all p, 1<p<\infty. Moreover, under certain assumptions on a family K of continuous functions, one change of variable will suffice for all f in  K. A similar result holds for functions on the torus T^d. This may be contrasted with the known result on the Wiener algebra, related to Luzin's rearrangement problem.