PreprintCC BY 4.0arXiv
Weighted boundedness of maximal operator associated with invertible linear transformations on variable Lebesgue spaces
Abstract
In this paper, we study the boundedness of MA−1, the maximal operator involves an invertible matrix, on the weighted variable spaces Lp(·)(w), where the weights are in an appropriate class. In general, we obtain the necessary conditions for the weight classes and exponents. However, for certain types of invertible matrices, we characterize the weights such that the boundedness holds.
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BibTeX
@misc{firnkorn2026weighted,
title = {{Weighted boundedness of maximal operator associated with invertible linear transformations on variable Lebesgue spaces}},
author = {Gonzalo H. Ibañez Firnkorn and Lucas A. Vallejos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30603},
eprint = {2610.30603},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30603},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Weighted boundedness of maximal operator associated with invertible linear transformations on variable Lebesgue spaces
AU - Gonzalo H. Ibañez Firnkorn
AU - Lucas A. Vallejos
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30603
UR - https://arxiv.org/abs/2610.30603
AB - In this paper, we study the boundedness of M_A^−1, the maximal operator involves an invertible matrix, on the weighted variable spaces L^p(·)(w), where the weights are in an appropriate class. In general, we obtain the necessary conditions for the weight classes and exponents. However, for certain types of invertible matrices, we characterize the weights such that the boundedness holds.
ER -