Hardy型算子在径向——角向混合空间上的最佳界  

Sharp Bounds for Hardy-type Operators on Mixed Radial-angular Spaces

作　　者：魏明权 燕敦验 WEI Mingquan;YAN Dunyan(School of Mathematics and Statistics,Xinyang Normal University,Xinyang,Henan,464000,P.R.China;School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing,100049,P.R.China)

机构地区：[1]信阳师范大学数学与统计学院,河南信阳464000 [2]中国科学院大学数学科学学院,北京100049

出　　处：《数学进展》2024年第1期151-161,共11页Advances in Mathematics（China）

基　　金：Supported by the NSFC(Nos.11871452,12301123);NSF of Henan Province(No.202300410338)。

摘　　要：本文运用旋转方法算出了n维Hardy算子H在径向—角向混合空间上的最佳界.进一步,当0<β<n,1<p,q,p,q<∞且1/p-1/q=β/n时,得到了n维分数次Hardy算子H_β从L|x|p L_θp(Rn)到L|x|qL_θq(Rn)上的最佳界.通过对偶建立了共轭算子H~*和H_(β)^(*)的相应结果.此外,还考虑了算子H的最佳弱型估计.In this paper,by using the rotation method,we calculate that the sharp bound for n-dimensional Hardy operator H on mixed radial-angular spaces.Furthermore,we also obtain the sharp bound for n-dimensional fractional Hardy operator H_βfrom L_(|x|)~pL_θ~p(R~n)to L_(|x|)~qL_θ~q(R~n),where 0<β<n,1<p,■,■<∞and■.using duality,the P q corresponding results for the dual operators H*and H*β are also established.In addition,the sharp weak-type estimate for H is also considered.

关 键 词：HARDY算子 最佳界 分数次Hardy算子 径向—角向混合空间 旋转方法 

分 类 号：O174.2[理学—数学]