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Rough maximal functions supported by subvarieties on Triebel–Lizorkin spaces

  • Feng Liu
Original Paper

Abstract

In this paper, we establish the boundedness of a class of maximal functions related to rough singular integrals supported by compound subvarieties on Triebel–Lizorkin spaces and Besov spaces. As applications, several corresponding estimates of maximal functions related to parametric Marcinkiewicz integrals are also presented.

Keywords

Singular integral Parametric Marcinkiewicz integral Maximal function Triebel–Lizorkin space Besov space 

Mathematics Subject Classification

42B20 42B15 42B25 

Notes

Acknowledgements

This work was partially supported by the NNSF of China (No. 11526122), Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (No. 2015RCJJ053), Research Award Fund for Outstanding Young Scientists of Shandong Province (No. BS2015SF012) and Support Program for Outstanding Young Scientific and Technological Top-notch Talents of College of Mathematics and Systems Science (No. Sxy2016K01). We would like to thank the referees very much for their invaluable comments and suggestions.

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Copyright information

© Springer-Verlag Italia 2017

Authors and Affiliations

  1. 1.College of Mathematics and Systems Science, Shandong University of Science and TechnologyQingdaoPeople’s Republic of China

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