THE FRACTIONAL TYPE MARCINKIEWICZ INTEGRALS AND COMMUTATORS ON WEIGHTED HARDY SPACES  

作　　者：韩妍妍 伍火熊 Yanyan HAN;Huoxiong WU(School of Mathematical Sciences,Xiamen University,Xiamen 361005,China)

机构地区：[1]School of Mathematical Sciences,Xiamen University,Xiamen 361005,China

出　　处：《Acta Mathematica Scientia》2023年第5期1981-1996,共16页数学物理学报（B辑英文版）

基　　金：supported by the NSFC(12171399,12271041).

摘　　要：This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β/n,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn).

关 键 词：fractional type Marcinkiewicz integrals COMMUTATORS Muckenhoupt weights BMO spaces Hardy spaces 

分 类 号：O177[理学—数学]