International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 9, Pages 533-540
Hardy-Littlewood type inequalities for Laguerre series
Department of Mathematics, National Central University, Chung-Li, 320, Taiwan, China
Received 30 August 2001
Copyright © 2002 Chin-Cheng Lin and Shu-Huey Lin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a null sequence of bounded variation. We give appreciate smoothness and growth conditions on to obtain the pointwise convergence as well as -convergence of Laguerre series . Then, we prove a Hardy-Littlewood type inequality for certain , where is the limit function of . Moreover, we show that if is in , , we have the converse Hardy-Littlewood type inequality for and .