Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774278 | Journal of Differential Equations | 2017 | 29 Pages |
Abstract
To strengthen the weak restriction principle discovered in both [2, Theorem 5.1] for λ=κ and [32, Lemma 2.1] for λ<κ, this paper shows that the Riesz operator Iα of order α maps the Morrey-Hardy space LHp,κ to the Morrey-Radon space Lμq,λ continuously if and only ifsup(x,r)âRnÃ(0,â)â¡Î¼(B(x,r))/rβ<âprovided{0<λâ¤Îºâ¤n;0<ακ>0 then the iff-statement fails. Quite remarkably, such an optimization confirms affirmatively the conjecture in [7, Remark 3.3]: ifα<αp<κ<λ=n&q=pβ/(κâαp) then there is no continuity of Iα:Lp,κâLμq,n for an arbitrary Radon measure μ with â¦Î¼â¦Î²<â.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
L. Liu, J. Xiao,