Carleson Type Theorems for Certain Convolution Operators

Abstract.

We prove mapping theorems for some convolution operators, acting from Sobolev type spaces in $\mathbb{R}^{n}$ to Lorentz spaces defined on $\mathbb{R}^{{n + 1}}_{ + }$ with a fractional-order Carleson measure. As an application of the major theorems, we give some a priori estimates for the solutions of certain elliptic equations.