BMO Boundedness for Banach Space Valued Singular Integrals

Abstract

In this paper, we consider a class of Banach space valued singular integrals. The $L^p$ boundedness of these operators has already been obtained. We shall discuss their boundedness from BMO to BMO. As applications, we get BMO boundedness for the classic $g$-function and the Marcinkiewicz integral. Some known results are improved.