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Contractivity of Rudin's diagonal restriction operator for Hp of the polydisc
Abstract
We establish that Rudin's diagonal restriction operator is contractive from the Hardy space Hp of the bidisc to the Bergman space Ap of the disc for 2≤ p<∞, 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 pth powers of the two Lp norms.
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BibTeX
@misc{brevig2026contractivity,
title = {{Contractivity of Rudin's diagonal restriction operator for $H^p$ of the polydisc}},
author = {Ole Fredrik Brevig and Javier Gómez-Serrano and Joaquim Ortega-Cerdà and Kristian Seip},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16227},
eprint = {2610.16227},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16227},
}
RIS
TY - UNPB
TI - Contractivity of Rudin's diagonal restriction operator for H^p of the polydisc
AU - Ole Fredrik Brevig
AU - Javier Gómez-Serrano
AU - Joaquim Ortega-Cerdà
AU - Kristian Seip
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16227
UR - https://arxiv.org/abs/2610.16227
AB - 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≤ p<∞, 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 pth powers of the two L^p norms.
ER -