Estimates of Lebesgue constants via Fourier transforms. Many dimensions

Details Estimates of Lebesgue constants via Fourier transforms. Many dimensions Estimates of Lebesgue constants via Fourier transforms. Many dimensions

1995-01-16

arxiv.org/abs/funct-an/9501003v2

Mathematics

Functional Analysis

41 pages, AMSTEX, no figures

Scientific paper

This is an attempt of a comprehensive survey of the results in which estimates of the norms of linear means of multiple Fourier series, the Lebesgue constants, are obtained by means of estimating the Fourier transform of a function generating such a method. Only few proofs are given in order to illustrate a general idea of techniques applied. Among the results are well known elsewhere as well as less known or published in an unacceptable journals and several new unpublished results.

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