Boundedness of certain singular integrals along surfaces on Triebel–Lizorkin spaces

Abstract

In this paper, we give a criterion of boundedness for the operators of convolution type on Triebel-Lizorkin spaces. As applications, under rather weak size conditions, the bounds for the singular integrals along certain compound surfaces on the above function spaces are obtained. Some previous results are improved and extended.

Rough singular integralsassociated to surfaces of revolutionon Triebel-Lizorkin spaces

“…The investigation of boundedness of T h,Ω,P on Triebel-Lizorkin spaces has attracted the attention of many authors. For relevant results, one may consult [6,22,23].…”