Boundedness of Marcinkiewicz integralwith rough kernel onTriebel-Lizorkin spaces

Abstract

This paper is a continuation of our previous work (Zhang and Chen, 2010b). Following the same general steps of the proof there, we make essential improvement on our previous theorem by recalculating a key inequality. Our result shows that the Marcinkiewicz integral, with a bounded radial function in its kernel, is still bounded on the Triebel-Lizorkin space.

Keywords

Marcinkiewicz integral / Triebel-Lizorkin spaces

References

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