International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 1, Pages 205-207

Generalizations of inequalities of littlewood and paley

Lou Zengjian

Mathematics Department, Qufu Normal University, Shandong, Qufu 273165, China

Received 30 July 1991; Revised 13 December 1991

Copyright © 1993 Lou Zengjian. 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.


For a function f, holomorphic in the open unit ball Bn in Cn, with f(0)=0, we prove (I) If 0<s2 and sp< Then fppC01Bn|f(ρζ)|ps|Rf(ρζ)|s(log1/ρ)s1ρ1dσ(ζ)dρ (ii) If 2Bp< Then 01Bn|f(ρζ)|ps|Rf(ρζ)|s(log1/ρ)s1ρ1dσ(ζ)dρCfpp where Rf is the radial dervative of f, generalizing the known cases p=s([1]) and p=s, n=1 ([2]).