BMO Space and its relation with wavelet theory

Subject Areas : Applied Mathematics

M. Ghanbari ^{1 *}

1 - Department of Mathematics, Islamic Azad University, Farahan-Branch, Farahan, Iran.

Received: 2015-10-05 Accepted : 2015-10-05 Published : 2012-12-01

Keywords: BMO space, wavelets, Orthonormal system, Rademacher system, Walsh system, Haar system,

Abstract :

The aim of this paper is a) if Σak2< ∞then Σak rk(x) is inBMO that{rk(x)} is Rademacher system. b) P1k=1 ak!nk (x) 2 BMO; 2k  nk < 2k+1that f!n(x)g is Walsh system. c) If jakj < 1k then P1k=1 ak!k(x) 2 BMO.