New Properties of Holomorphic Sobolev–Hardy Spaces

William Gryc; Loredana Lanzani; Jue Xiong; Yuan Zhang

doi:10.1007/s11785-024-01637-8

New Properties of Holomorphic Sobolev–Hardy Spaces

William Gryc, Loredana Lanzani, Jue Xiong, Yuan Zhang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We give new characterizations of the optimal data space for the Lp(bD,σ)-Neumann boundary value problem for the ∂¯ operator associated to a bounded, Lipschitz domain D⊂C. We show that the solution space is embedded (as a Banach space) in the Dirichlet space and that for p=2, the solution space is a reproducing kernel Hilbert space.

Original language	English (US)
Article number	13
Journal	Complex Analysis and Operator Theory
Volume	19
Issue number	1
DOIs	https://doi.org/10.1007/s11785-024-01637-8
State	Published - Dec 2024

Keywords

Lipschitz domain
Neumann problem
Reproducing kernel Hilbert space
Sobolev–Hardy space
∂¯

ASJC Scopus subject areas

Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

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10.1007/s11785-024-01637-8

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keywords = "Lipschitz domain, Neumann problem, Reproducing kernel Hilbert space, Sobolev–Hardy space, ∂¯",

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AB - We give new characterizations of the optimal data space for the Lp(bD,σ)-Neumann boundary value problem for the ∂¯ operator associated to a bounded, Lipschitz domain D⊂C. We show that the solution space is embedded (as a Banach space) in the Dirichlet space and that for p=2, the solution space is a reproducing kernel Hilbert space.

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KW - Sobolev–Hardy space

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New Properties of Holomorphic Sobolev–Hardy Spaces

Abstract

Keywords

ASJC Scopus subject areas

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