Hardy-Littlewood type inequalities for laguerre series

Chin Cheng Lin, Shu Huey Lin

Research output: Contribution to journalArticlepeer-review


Let { cj} be a null sequence of bounded variation. We give appreciate smoothness and growth conditions on {c j} to obtain the pointwise convergence as well as L r-convergence of Laguerre series Σcj&Lfr;ja. Then, we prove a Hardy-Littlewood type inequality ∫0 | f (t)| rdt≤CΣ j=0 | cj| rj- 1-r/2 for certain r≤1, where f is the limit function of Σcj&Lfr;ja. Moreover, we show that if f (x)∼Σcj&Lfr;ja is in L r, r≥1, we have the converse Hardy-Littlewood type inequality Σ j=0 | cj| rj -β≤ C∫0 | f (t)| rdt for r≥1 and β<-r/2.

Original languageEnglish
Pages (from-to)533-540
Number of pages8
JournalInternational Journal of Mathematics and Mathematical Sciences
Issue number9
StatePublished - 2002


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