The Boundedness Of The Intrinsic Square Function In The Weighted Variable Exponential Space

In this thesis,we introduced the weighted Herz-Morrey spaces and Morrey spaces with variable exponents.By using the boundedness of intrinsic square functions on weighted Lebesgue space with variable exponent,applying the real variable method of harmonic analysis,the properties of variable exponents and weight functions,as well as the characteristics of Herz-Morrey spaces and Morrey spaces with variable exponents,and estimating the inequality,we obtained the boundedness of intrinsic square function and vector-valued intrinsic square function on weighted Herz-Morrey spaces with variable exponents.Moreover,we showed the boundedness of intrinsic square functions on weighted Morrey spaces with variable exponents.