J Austral Math Soc Ser A 46 pp289--295, 1989.

On an Equivalent Class of Norms for BMO

Yong-Zhou Chen and Ka-Sing Lau

Abstract

The BMO norm of f is equivalent to

sup (x,t) Î R+n+1 æ è ó õ |f(y) - u(x,t)|pPt(x - y)dy ö ø 1/p   ,

where P_t is the Poisson kernel. In this note, we show that P_t can be replaced by a nonnegative radial function h, which is positive in a neighbourhood of 0, with ò_(Rⁿ)h(x)dx = 1 and ò₁^¥ r^n-1(ln r)^p~h(r)dr < ¥ where~h is the least decreasing radial majorant of h.

1980 AMS Subject Classification (1985 Revision): primary 42B30; secondary 42B99

Browse the article

Authors

Yong-Zhuo Chen

Ka-Sing Lau

Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403, U.S.A.