Some Operators And Their Commutators On Variable Exponent Herz Type Spaces

In this paper,we mainly study the boundedness of some operators and their commu-tators on variable exponent Herz type spaces.In chapter one,the history,development,signification and evolving of the theory of variable exponent Herz type spaces are reviewed.In chapter two,by using the atomic decomposition of the varnable exponent Herz-type Hardy spaces,we obtain the boundedness of the fractional integral operators with varnable kernel and their higher order commutators generated by these operators and Lip-schitz functions on variable exponent Herz-type Hardy spaces.In addition,the bound-edness of the higher order commutators generated by the fractional integral operators with variable kernel and Lipschitz functions on variable exponent Herz-Morrey spaces are proved.In chapter three,applying the atomic decomposition theorem,we get the bounded-ness of the Calderon-Zygmund singular integral operators with rough kernel and their commutators generated by these operators and BMO functions on Herz-Morrey-Hardy spaces with variable exponent.