PreprintarXiv licencearXiv
Characterization of the boundedness of the segment multiplier on weighted Lebesgue spaces
Abstract
For 1<p<∞, we characterize the boundedness of the segment multiplier on Lp(w) by a large-scale Muckenhoupt condition, obtained by restricting the classical Ap 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
@misc{bareafernandez2026characterization,
title = {{Characterization of the boundedness of the segment multiplier on weighted Lebesgue spaces}},
author = {Miguel F. Barea-Fernández and Jan Lang and Javier Soria},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32039},
eprint = {2609.32039},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32039},
}
RIS
TY - UNPB
TI - Characterization of the boundedness of the segment multiplier on weighted Lebesgue spaces
AU - Miguel F. Barea-Fernández
AU - Jan Lang
AU - Javier Soria
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.32039
UR - https://arxiv.org/abs/2609.32039
AB - For 1<p<∞, 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.
ER -