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Working paper

Homeomorphic Changes of Variable and Fourier Multipliers

arxiv.org. math. Cornell University, 2019. No. arXiv:1803.02177v2.
Lebedev V., Olevskii A.
We consider the algebras M_p of Fourier multipliers and show that for every bounded continuous function f on R^d there exists a self-homeomorphism h of R^d such that the superposition f oh is in M_p(R^d) for all p, 1 < p < \infty. Moreover, under certain assumptions on a family K of continuous functions, one h will sffice for all f in 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.