变指标函数空间的进展

Recent Developments of Function Spaces With Variable Exponents

本文先综述(局部)Hardy-Littlewood极大算子,(变)分数阶积分算子在变指标Lebesgue空间上的有界性.然后综述了变指标空间的进展,如变指标Besov和Triebel-Lizorkin空间、Morrey型的变指标Besov和Triebel-Lizorkin空间、变指标Herz型的Besov和Triebel-Lizorkin空间、变指标Hardy空间、变指标Herz型Hardy空间等.同时提出几个未解决的问题.

In this paper,we give a summary of the boundedness of(local) Hardy-Littlewood maximal operator and(variable) fractional integrals on variable Lebesgue spaces.Then we present recent developments of the theory of function spaces with variable exponents,which include Besov and Triebel-Lizorkin spaces,Morrey type Besov and Triebel-Lizorkin spaces,Herz type Besov and Triebel-Lizorkin spaces,Hardy spaces and Herz type Hardy spaces with variable exponents.Along the way several open problems are also given.