The Wavelet Characterization And Application Of Herz-Morrey-Hardy Space With Variable Index

In this thesis,firstly,the definitions and basic properties of the variable exponents Lebesgue spaces,Herz-Morrey spaces and Herz-Morrey-Hardy spaces are given.Then,a kind of discrete tent spaces with variable exponents is introduced.And the characterization of the tent spaces in terms of atoms is established.Based on the atomic decomposition of the Herz-Morrey-Hardy spaces with variable exponents,by the properties of the variable exponents and by means of a local version of the discrete tent spaces with variable exponent,the main result,the wavelet characterization of the Herz-Morrey-Hardy spaces with variable exponents is proved.Finally,as an application,the boundedness of the fractional integral operators from variable exponent Herz-Morrey-Hardy spaces into variable exponent Herz-Morrey spaces is obtained.