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arXiv · 2511.11312

Approximation via partial Hausdorff integrals on $H^1(\mathbb{R})$

Zifei Yu·Baode Li
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Abstract

We obtain the result of approximating \( f \) in the \( H^1(\mathbb{R}) \) norm using partial Hausdorff integrals. Specifically, by leveraging the homogeneous multiplier theory of \( H^1(\mathbb{R}) \) and the \( K \) functional theory, one result from Pinos and Liflyand [CMB,~2021,~64,~no.3] is extended from \( L^p(\mathbb{R}) \) ( \( 1 \leq p \leq \infty \)) to \( H^1(\mathbb{R}) \). As applications, four examples of partial Hausdorff integrals are also given.

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Zifei Yu, Baode Li. 2025-11-14. Approximation via partial Hausdorff integrals on $H^1(\mathbb{R})$. https://arxiv.org/abs/2511.11312

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