Characterization of the boundedness of the segment multiplier on weighted Lebesgue spaces

Miguel F. Barea-Fernández; Jan Lang; Javier Soria

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arXiv · 2609.32039

Characterization of the boundedness of the segment multiplier on weighted Lebesgue spaces

Miguel F. Barea-Fernández·Jan Lang·Javier Soria

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Abstract

For $1<p<\infty$, we characterize the boundedness of the segment multiplier on $L^p(w)$ by a large-scale Muckenhoupt condition, obtained by restricting the classical $A_p$ condition to intervals of length at least one. The proof uses a discretization involving the discrete Hilbert transform on an associated weighted sequence space.

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BibTeX RIS

Miguel F. Barea-Fernández, Jan Lang, Javier Soria. 2026-09-25. Characterization of the boundedness of the segment multiplier on weighted Lebesgue spaces. https://arxiv.org/abs/2609.32039

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