Localized Haar Extensions on the Dyadic Plane
Year: 2026
Type: preprint
Abstract: We prove that every $L^2$ function on a set $E\subset\mathbb R^2$ of finite measure can be extended linearly to the whole plane using Haar functions. The extension agrees with the original function on $E$, with uniform bounds on its norm and the total area of the Haar rectangles used. In particular, we construct a function equal to $1$ on any finite-measure open set, satisfying the dyadic Hardy norm estimates for all $0
Author: Gao, Shu
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223477438
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