The Leray transform: distinguished measures, symmetries and polygamma inequalities

Abstract

New symmetries, norm computations and spectral information are obtained for the Leray transform on a class of unbounded hypersurfaces in ${\mathbb{C}}^2$. Emphasis is placed on certain distinguished measures, with results on operator norm monotonicity established by proving new polygamma inequalities. Classical techniques of Bernstein-Widder and Euler-Maclaurin play crucial roles in our analysis. Underpinning this work is a projective geometric theory of duality, which manifests here in the form of Hölder invariance.

30 pages, 2 figures with 10 total graphs, 4 tables. A carefully notated Mathematica notebook to help walk the reader through difficult calculations in Section 5 and the Appendix can be found on the first author's Github page: https://github.com/ledholm/Leray-measures-2024-Mathematica-nb/releases/tag/v1.0

References in corpus (3)

• The Leray transform: factorization, dual $CR$ structures and model hypersurfaces in $\mathbb{C}{\mathbb{P}}^2$
• High frequency behavior of the Leray transform: model hypersurfaces and projective duality
• The Kerzman-Stein operator for piecewise continuously differentiable regions