International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1994 / Article

Open Access

Volume 17 |Article ID 679145 | https://doi.org/10.1155/S016117129400027X

Zengjian Lou, "Extensions of Hardy-Littlewood inequalities", International Journal of Mathematics and Mathematical Sciences, vol. 17, Article ID 679145, 3 pages, 1994. https://doi.org/10.1155/S016117129400027X

Extensions of Hardy-Littlewood inequalities

Received30 Dec 1992
Revised13 May 1993

Abstract

For a function fHp(Bn), with f(0)=0, we prove(1) If 0<ps,then01r1(log1r)sβ1Mps(r,Rβf)drfpspfp,s,βp(2) If sp<, thenfp,s,βpfpps01r1(log1r)sβ1Mps(r,Rβf)drwhere Rβf is the fractional derivative of f. These results generalize the known cases s=2, β=1 ([1]).

Copyright © 1994 Hindawi Publishing Corporation. 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.


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