Continuity of the mean values of BMO functions and Calderon-Zygmund properties of certain singular integrals

Abstract

In this note we shall show that certain bilinear singular integrals T(a,f) with symmetric property in some sense are bounded bilinear operators from BMO× Lp into Lp, more precisely, for any BMO function a the operator T(a,・) is a Calderon-Zygmund singular integral operator (Theorems 1 and 2). These results are, in a sense, extensions of the relating results in Baishansky and Coifman [1]. To prove the above, the Holder continuity of the mean values of BMO functions