Hypercontractive inequalities for weighted Bergman spaces

被引：1
|
作者：
Melentijevic, Petar [1 ,2 ]
机构：
[1] Univ Belgrade, Matemat Fak, Dept Real & Funct Anal, Belgrade, Serbia
[2] Univ Belgrade, Matemat Fak, Dept Real & Funct Anal, Studentski Trg 16, Belgrade 11000, Serbia
来源：
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2023年 / 55卷 / 06期
关键词：
SOBOLEV INEQUALITIES;
D O I：
10.1112/blms.12883
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We obtain sharp Lp & RARR;Lq$L<^>p\rightarrow L<^>q$ hypercontractive inequalities for the weighted Bergman spaces on the unit disk D$\mathbb {D}$ with the usual weights & alpha;-1 & pi;(1-|z|2)& alpha;-2,& alpha;>1$\frac{\alpha -1}{\pi }{(1-|z|<^>2)}<^>{\alpha -2},\alpha >1$ for q & GT;2$q\geqslant 2$, thus solving an interesting case of a problem from Janson [Ark. Math. 21 (1983), no. 1, 97-110]. We also give some estimates for 0<q<2$0<q<2$.
引用
收藏
页码：2611 / 2616
页数：6
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