CERTAIN FRACTIONAL TYPE OPERATORS WITH HORMANDER CONDITIONS

In this paper we study fractional type operators with more than one kernel, defined by T(alpha,m)f(x) = integral(Rn )k(1)(x - A(1y))k(2)(x - A(2y)) ... k(m)(x - A(my)) f(y)dy, where, for 1 <= i <= m, each k(i) satisfies a fractional size condition and generalized fractional Hormander condition, and A(i) 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.