A General Theorem on Lebesgue Constants

E. Liflyand

Research output: Contribution to journalArticlepeer-review


A very general asymptotic type formula is presented for the Lebesgue constants of both Fourier partial sums and linear methods of summability of Fourier series in the multivariate Euclidean spaces. More precisely, the obtained formula represents the norm of a trigonometric polynomial with coefficients being the values of a multiplier as the norm of the Fourier transform of this multiplier, with an error which in many cases (after appropriate estimates) leads either to a really asymptotic relation or to a suitable upper estimate.

Original languageEnglish
Pages (from-to)435-442
Number of pages8
JournalJournal of Mathematical Sciences
Issue number4
StatePublished - Dec 2022

Bibliographical note

Funding Information:
This work is financially supported and performed under the auspices of the Iran National Science Foundation and the University of Tarbiat Modares in the program of postdoctoral research projects.

Publisher Copyright:
© 2022, Springer Science+Business Media, LLC, part of Springer Nature.


Dive into the research topics of 'A General Theorem on Lebesgue Constants'. Together they form a unique fingerprint.

Cite this