Boundedness Of Some Operators On The Variable Lorentz Spaces

In this thesis,we mainly study the boundedness of some operators on the variable Lorentz spaces and obtain the sufficient conditions for the boundedness of some classical operators in harmonic analysis.In addition,we also give the estimates of the semigroup of fractional heat operators and nonlinear term of the fractional power dissipative equations.The thesis is divided into three chapters.In the first chapter we introduce the development and background of the variable Lebesgue spaces,the variable Lorentz spaces and the fractional power dissipative equations,then give the main results of this thesis.In the second chapter we review the definitions and properties of the rearrangement functions,the variable Lebesgue spaces and the variable Lorentz spaces,then give the lemmas that will be used.In the third chapter by properties of the weighted Hardy operators on the variable Lebesgue spaces,we obtain the boundedness of some classical operators on the variable Lorentz spaces.In addition,we also obtain the estimates of the semigroup of fractional heat operators and nonlinear term of the fractional power dissipative equations.