%0 Journal Article
%T LEBESGUE CONSTANTS OF MULTIPLE FOURIER SERIES
%A E. R. Liflyand
%J Online Journal of Analytic Combinatorics
%D 2006
%I University of Auckland
%X This is an attempt of a comprehensive treatment of the results concerning estimates of the $L^1$-norms of linear means of multiple Fourier series, the Lebesgue constants. Most of them are obtained by estimating the Fourier transform of a function generating such a method. Frequently the properties of the support of this function affects distinctive features in behavior of these norms. By this geometry enters and works hand-in-hand with analysis; moreover, the results are classified mostly in accordance with their geometrical nature. Not rarely Number Theory tools are brought in. We deal only with the trigonometric case - no generalizations for other orthogonal systems are discussed nor are applications to approximation. Several open problems are posed.
%U http://analytic-combinatorics.org/index.php/ojac/article/view/9