Analytic extensions of $A_{\infty}$-weights on Lipschitz curves and their use in weighted Hardy spaces
Year: 2025
Type: preprint
Abstract: An $A_{\infty}$-weight on a Lipschitz curve $Λ$ in the plane can be extended analytically to the graph Lipschitz domain $Ω$ above it. This problem was studied by C. Kenig [Ken80], who introduced the class $AE$ of well-behaved analytic extensions. Later, he and D. Jerison [JK82] added a Smirnov-type condition to the definition of this class. In this note, we show that this Smirnov-type condition is equivalent to an $H^1$-integrability condition. As a consequence, one of the conditions in the definition of $AE$ can be dropped. We use this simplification to apply C. Kenig's theory to prove results about weighted Hardy spaces. These are useful to study the Neumann problem in $Ω$ with boundary data in weighted spaces.
Source: arXiv (Cornell University)
Author: Ballesta-Yagüe, Fernando
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416259901
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