Bergman spaces of natural \(G\)-manifolds

DOI10.1016/J.AIM.2013.07.012zbMath1293.32009arXiv1205.5154OpenAlexW2062644058WikidataQ42645562 ScholiaQ42645562MaRDI QIDQ2437559

Giuseppe Della Sala, Joe J. Perez

Publication date: 3 March 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.5154

zbMATH Keywords

Bergman spacesholomorphic peak functionsfree actions of Lie groupsrepresentation of unimodular Lie groups

Mathematics Subject Classification ID

Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) (overlinepartial) and (overlinepartial)-Neumann operators (32W05) Bergman spaces of functions in several complex variables (32A36) Peak functions (32T40)

Cites Work

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• Unitary representations of unimodular Lie groups in Bergman spaces
• Essential self-adjointness, generalized eigenforms, and spectra for the \(\bar {\partial}\)-Neumann problem on G-manifolds
• The \(G\)-Fredholm property of the \(\bar{\partial}\)-Neumann problem
• Holomorphic \(L^2\) functions on coverings of pseudoconvex manifolds
• Generalized Fredholm properties for invariant pseudodifferential operators
• Harmonic integrals on strongly pseudo-convex manifolds. II
• The Levi problem on strongly pseudoconvex \(G\)-bundles
• A transversal Fredholm property for the $\bar\partial$-Neumann problem on $G$-bundles
• Q.U.P. and Paley-Wiener properties of unimodular, especially nilpotent, Lie groups
• Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group
• Lie groups beyond an introduction

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