Grand Morrey Spaces Estimates For Parabolic Equations With VMO Coefficients

In this paper, by using the method of harmonic analysis and the solution representation formula of parabolic equation, we estimate the uniqueness and regularity of the solution in grand morrey spaces.The individual chapters are scheduled as follows:Chapter 1:We will introduce the theory of harmonic analysis which applies for partial differential equation and the current research circumstance on the theory of it and introduce the main theorems which would be proved afterward are listed in this chapter.Chapter 2:The estimation of maximal operator and sharp maximal operator in grand morrey spaces.Chapter 3:The estimation of the singular integral operator and commutators in grand morrey spaces.Chapter 4:The estimation of the non-singular integral operator and commutators in grand morrey spaces.Chapter 5: Grand morrey spaces estimates for parabolic equations with vmo coefficients.Chapter 6: Further study in the future.