Decomposition in blocks at the level of wavelet coefficients andT(1) theorem on Hardy space

This paper deals with the establishment ofT(1) theorem on Hardy spaceH ¹ under condition of weak regularity. An operator or a function is identified on the basis of their wavelet coefficients which are regrouped on some blocks. The actions of each block operator (pseudo-annular operator) on each block function (atom) are exactly analyzed to establishT(1) theorem on Hardy space. Project supported by the National Natural Science Foundation of China (No. 1000102) and Education Ministry of China.