Weighted $L^p$-boundedness of convolution type integral operators associated with bilinear estimates in the Sobolev spaces

Abstract

We study the boundedness of integral operators of convolution type in the Lebesgue spaces with weights. As a byproduct, we give a simple proof of the fact that the standard Sobolev space $H^s(\mathbb{R}^n)$ forms an algebra for $s$ > $n/2$. Moreover, an optimality criterion is presented in the framework of weighted $L^p$-boundedness.