Work

Contractivity of Rudin's diagonal restriction operator for $H^p$ of the polydisc

Year: 2026

Type: preprint

Abstract: We establish that Rudin's diagonal restriction operator is contractive from the Hardy space $H^p$ of the bidisc to the Bergman space $A^p$ of the disc for $2\leq p<\infty$, and characterize all cases of equality. We extend the result to polydiscs and obtain applications to polynomial point evaluation among others. The proof relies on an explicit formula, deduced from certain Green's formulas, for the defect between the $p$th powers of the two $L^p$ norms.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.16227

Authors: Brevig, Ole Fredrik, Gómez-Serrano, Javier, Ortega-Cerdà, Joaquim, Seip, Kristian

Institution: Brown University

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7221825641

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