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 $C^2$. 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.