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 C2. 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 H\"older invariance.
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