ON A HARDY-LITTLEWOOD THEOREM

E. Liflyand, STADTMULLER U.

Research output: Contribution to journalArticlepeer-review

Abstract

A known Hardy-Littlewood theorem asserts that if both the function and its conjugate are of bounded variation, then their Fourier series are absolutely convergent. It is proved in the present paper that the same result holds true for functions on the whole axis and their Fourier transforms, with certain adjustments. The proof of the original Hardy-Littlewood theorem is derived from the obtained assertion. It turned out that the former is a partial case of the latter when the function is supposed to be of compact support. A similar result for radial functions is derived from the one-dimensional case.
Original languageAmerican English
Pages (from-to)481-489
Number of pages9
JournalBulletin of the Institute of Mathematics Academia Sinica
Volume8
Issue number4
StatePublished - 2013

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