Boundedness Of The Bochner-riesz Operators On Variable Exponential Spaces

This thesis investigate the boundedness of the commutator generated by Bochner-Riesz o perator on Lebesgue and its weighted spaces with variable exponent,and further explores the boundedness of the commutator of Bochner-Riesz operator with variable exponential Lispchit z function and BMO function on the Herz-Morrey space with variable exponent and the bound edness of the higher-order commutator of Bochner-Riesz operator and Lispchitz function on th e variable exponential Herz-Morrey.In Chapter 1,we discribes the research background and significance of this paper,and the n gives the symbolic expressions and concepts throughout the paper.In Chapter 2,the boundedness of r-order fractional maximal operators can obtained by th e boundedness of Hardy-Littlewood maximal operators through making use of the norm prope rties of variable exponential Lebesgue and its weighted spaces.Combining with sharp inequali ty,we explore the boundedness of the commutator generated by Bochner-Riesz operator on Le besgue and its weighted spaces with variable exponent.In Chapter 3,using the ring decomposition principle to break down the commutator gene rated by the Bochner-Riesz operator and variable exponential Lipschitz function b(x)into thre e parts,and estimate the boundedness of the three parts through the properties of Lipschitz fun ction with variable exponent,we prove the boundedness of the commutator of Bochner-Riesz operator and variable exponential Lispchitz function on the Herz-Morrey space with variable e xponent.Besides,the correspond situation of the maximal operator and the commutator of the Bochner-Riesz operator with BMO function can be deduced.In Chapter 4,under the guidance of the conclusion and the method attained in Chapter 2 and Chapter 3,we obtained the boundedness of higher-order commutators generated by Bochn er-Riesz operators and Lipschitz functions on weighted Herz Morrey spaces with variable exp onent.