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The optimal hypercontractive constants for and biased Bernoulli random variables
Jie Cao, Shilei Fan, Yong Han +2
We resolve a folklore problem of determining the optimal hypercontractive constants for the cyclic group for all . More p…
Hypercontractive inequalities and Nikol'ski\uı-type inequalities on weighted Bergman spaces
Zipeng Wang, Kenan Zhang
In this note, we obtianed hypercontractive inequalities between different weighted Bergman spaces. In addition, we establish Nikol'ski\uı-type inequalities for weighted Bergman sp…
The one-weight inequality for -harmonic Bergman projection
Kunyu Guo, Zipeng Wang, Kenan Zhang
Let be an integer. For the Bekollé-Bonami weight on the real unit ball , we obtain the following sharp one-weight estimate for the -…
Weighted inequality of integral operators induced by Hardy kernels
Zipeng Wang, Kenan Zhang
For doubling weights, we obtain a necessary and sufficient condition such that the one weighted inequality of the integral operator induced by Hardy kernels on the unit disk holds.…