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

This paper deals with the establishment of T(1) theorem on Hardy space H1 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 establish T(1) theorem on Hardy space.