A decrease in growth of Lebesgue constants

E. Liflyand

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3 Scopus citations


The Lebesgue constants of cubic partial sums of order N of n-dimensional Fourier series behave asymptotically as lnn N. For cubic linear means generated by a function vanishing only at 2n corner points the order of growth of the Lebesgue constants decreases and equals asymptotically to lnn-1 N. This generalizes Kivinukk's results where the ordinary estimates were given.

Original languageEnglish
Pages (from-to)20-29
Number of pages10
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - 1 Aug 1997

Bibliographical note

Funding Information:
* The author acknowledges the support of the Minerva Foundation in Germany through the Emmy Noether Mathematics Institute in Bar-Ilan University. E-mail address: liflyand @macs.biu.ac.il.


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