Sharp quantitative integral inequalities for harmonic extensions
Rupert L. Frank, Jonas W. Peteranderl, Larry Read
TL;DR
This paper establishes a precise quantitative inequality for harmonic extensions, providing optimal stability exponents and strengthening previous results for the Poisson operator and its adjoint.
Contribution
It introduces the strongest possible norm and the optimal stability exponent for a sharp integral inequality related to harmonic extensions, extending prior work.
Findings
Proves a quantitative version of a sharp integral inequality.
Identifies the optimal stability exponent, not necessarily equal to 2.
Demonstrates the inequality's strength for both the Poisson operator and its adjoint.
Abstract
We prove a quantitative version of a sharp integral inequality by Hang, Wang, and Yan for both the Poisson operator and its adjoint. Our result has the strongest possible norm and the optimal stability exponent. This stability exponent is not necessarily equal to 2, displaying the same phenomenon that Figalli and Zhang observed for the -Sobolev inequality.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Nonlinear Partial Differential Equations · Numerical methods in inverse problems