Hypercontractive inequalities and Nikol'ski\u{\i}-type inequalities on weighted Bergman spaces
Zipeng Wang, Kenan Zhang
TL;DR
This paper establishes hypercontractive inequalities and Nikol'ski2f-type inequalities with optimal constants for weighted Bergman spaces, advancing the understanding of function space relationships.
Contribution
It introduces new hypercontractive and Nikol'ski2f-type inequalities for weighted Bergman spaces with optimal constants, a novel contribution to the field.
Findings
Hypercontractive inequalities between weighted Bergman spaces
Nikol'ski2f-type inequalities with optimal constants
Enhanced understanding of weighted Bergman space relationships
Abstract
In this note, we obtianed hypercontractive inequalities between different weighted Bergman spaces. In addition, we establish Nikol'ski\u{\i}-type inequalities for weighted Bergman spaces with optimal constants.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Harmonic Analysis Research · Geometry and complex manifolds