A note on the boundedness of Calderón–Zygmund operators on Hardy spaces

Abstract

It was well known that Calderón–Zygmund operators T are bounded on H p for n n + ε < p ⩽ 1 provided T ∗ ( 1 ) = 0 . A new Hardy space H b p , where b is a para-accretive function, was introduced in [Y. Han, M. Lee, C. Lin, Hardy spaces and the Tb-theorem, J. Geom. Anal. 14 (2004) 291–318] and the authors proved that Calderón–Zygmund operators T are bounded from the classical Hardy space H p to the new Hardy space H b p if T ∗ ( b ) = 0 . In this note, we give a simple and direct proof of the H p − H b p boundedness of Calderón–Zygmund operators via the vector-valued singular integral operator theory.