The Boundedness of Marcinkiewicz Integrals and Multipliers and Their Commutators with Non-doubling Measures
|School||Jiangxi Normal University|
|Keywords||RBMO(μ) space Lp,λ（μ） space Marcinkiewicz integral Lp,Φ（Rn） space Lip(β) space multiplier commutator|
In this paper, we study the boundedness of Marcinkiewicz integrals and Multiplier with non-doubling measures. This paper is constituted with four chapters.In chapter 1. we introduce the background and main results about Marcinkiewicz integrals, multiplier and their commutators. We also illustrate how this topics come out.In chapter 2, we present the boundedness of Marcinkiewicz integrals which was introduced by Stein and that of the commutators of Marcinkiewicz integrals, which is introduced by Torchinsky and Wang, on Morrey spaces Lp,λ(μ) with non-doubling measures. This paper has been submitten to Applied Math A Jounal of chinese universities.In chapter 3. we consider the boundedness of Marcinkiewicz integrals and the commutators of Marcinkiewicz integrals with non-doubling Measures on Morrey space. This paper will be published in Acta Math Scientia (chinese),2011,31(3).In chapter 4, we discusses briefly the boundedness of multipliers and its commutators on some Morrey spaces, which appeared in Acta Math sinica (chinese),2011,54(1):81-88.