Certain fractional type operators with hörmander conditions

Abstract

In this paper we study fractional type operators with more than one kernel, defined by Tα,mf(x) = ˆRn k1(x − A1y)k2(x − A2y). . . km(x − Amy)f(y) dy, where, for 1 ≤ i ≤ m, each ki satisfies a fractional size condition and generalized fractional Hörmander condition, and Ai are invertibles matrices. We obtain weighted Coifman type estimates, strong and weak type inequalities and BMO estimates for this operator. We also present some examples different from those in the literature.