Lebesgue constants of multiple Fourier series

E. Liflyand

Research output: Contribution to journalArticlepeer-review


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.
Original languageAmerican English
Pages (from-to)1-112
JournalOnline Journal of Analytic Combinatorics
Issue number5
StatePublished - 2006

Bibliographical note

Article 5, 112 p.


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