BMO Space and its relation with wavelet theory

Abstract

The aim of this paper is a) if Σa_k²< ∞ then Σa_kr_k(x) is in BMO that<br />{r_k(x)} is Rademacher system. b) P1k=1 ak!nk (x) 2 BMO; 2k nk < 2k+1<br />that f!n(x)g is Walsh system. c) If jakj < 1<br />k then P1k=1 ak!k(x) 2 BMO.