\(L^2\) estimates and existence theorems for the \(\overline{\partial}\) operators in infinite dimensions. I

DOI10.1016/j.matpur.2022.05.013zbMath1497.46052arXiv2002.02260OpenAlexW4280496048WikidataQ113869064 ScholiaQ113869064MaRDI QIDQ2145843

Jiayang Yu, Zhang, X.

Publication date: 15 June 2022

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.02260

zbMATH Keywords

solvabilityGaussian measureinfinite dimensions\(\bar{\partial}\) equation\(L^2\) method

Mathematics Subject Classification ID

Infinite-dimensional holomorphy (46G20) Derivatives of functions in infinite-dimensional spaces (46G05) Calculus of functions on infinite-dimensional spaces (26E15)

Related Items

Sobolev embeddings in infinite dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The analytic embedding of abstract real-analytic manifolds
• Complex Neumann problems
• \(L^ 2\)-cohomology and index theorem for the Bergman metric
• The \(\bar\partial\)-problem for a (0,2)-form in a D.F.N. space
• Analyticity in infinite dimensional spaces
• Invariance of plurigenera
• An estimate for the Bergman distance on pseudoconvex domains
• Analyticity of sets associated to Lelong numbers and the extension of closed positive currents
• Lectures on the \(L^2\)-Sobolev theory of the \(\bar\partial\)-Neumann problem
• A solution of an \(L^{2}\) extension problem with an optimal estimate and applications
• An introduction to infinite-dimensional analysis
• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
• Harmonic integrals on strongly pseudo-convex manifolds. I
• Harmonic integrals on strongly pseudo-convex manifolds. II
• The \(\bar \partial\) equation with polynomial growth on a Hilbert space
• Le problème du $\overline\partial$ sur un espace de Hilbert
• A unified controllability/observability theory for some stochastic and deterministic partial differential equations
• Domains of convergence for monomial expansions of holomorphic functions in infinitely many variables
• Holomorphic Mappings on l 1
• The Dolbeault complex in infinite dimensions II
• The Dolbeault complex in infinite dimensions I
• Plurisubharmonic domination
• On the $\overline\partial$-equation in a Banach space
• Recent developments in infinite dimensional holomorphy
• L² Approaches in Several Complex Variables
• Measure Theory
• General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions
• The Neumann Problem for the Cauchy-Riemann Complex. (AM-75)
• Complex Boundary Value Problems
• On a Differential-Geometric Method in the Theory of Analytic Stacks
• The Dolbeault complex in infinite dimensions. III: Sheaf cohomology in Banach spaces

This page was built for publication: \(L^2\) estimates and existence theorems for the \(\overline{\partial}\) operators in infinite dimensions. I