Lorentz Estimates For Calderón-Zygmund Type Singular Integral Operators

Lorentz estimate is a new regularity estimate in the partial differential equations.In this paper,we mainly use Vitali covering lemma and level set to study Lorentz estimates for Calderón-Zygmund type singular integral operators.We divide this paper into four parts.The first chapter is the preface of the thesis.Here we mainly introduce the research background and regularity estimates of partial differential equations.Then,we extend regularity estimates to Calderón-Zygmund type singular integral operators in Harmonic analysis.The second chapter is the preliminary knowledge of this paper,including some basic concepts,basic inequalities and important lemmas in partial differential equations.In the third chapter,we mainly study Lorentz estimates for Calderón-Zygmund type singular integral operatorsIn the last chapter,we mainly summarize our main achievements in our paper,and present some further problems so as to investigate the follow-up work.