Triebel-lizorkin spaces of para-accretive type and a T b theorem

In this article, we use a discrete Calderón-type reproducing formula and Plancherel-Pôlya-type inequality associated to a para-accretive function to characterize the Triebel-Lizorkin spaces of para-accretive type F· ^a,q _b,p , which reduces to the classical Triebel-Lizorkin spaces when the para-accretive function is constant. Moreover, we give a necessary and sufficient condition for the F· ^0,q _1,p -F· ^0,q _b,p boundedness of paraproduct operators. From this, we show that a generalized singular integral operator T with MbTMb ε WBP is bounded from F· ^0,q _1,p to F· ^0,q _b,p if and only if T b ε F· ^0,q _b,∞ and T *b = 0 for n/n+e <p = 1 and n/ n+e <q ≤ 2, where e is the regularity exponent of the kernel of T.