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Working paper

Uniformly convergent Fourier series and multiplication of functions

arxiv.org. math. Cornell University, 2018. No. arXiv:1807.03949v1.
Let U(T) be the space of all continuous functions on the circle T whose Fourier series converges uniformly. Salem's well-known example shows that a product of two functions in U(T) does not always belongs to U(T) even if one of the factors belongs to the Wiener algebra A(T). In this paper we consider pointwise multipliers of the space U(T), i.e., the functions m such that mf is in U(T) whenever f is in U(T). We present certain sufficient conditions for a function to be a multiplier and also obtain some results of Salem type.