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Some weighted modular inequalities in variable Lebesgue spaces
Abstract
We establish a necessary and sufficient weight condition so that a modular inequality holds for a generalized integral operator Tϕ on non-negative non-increasing functions in weighted variable Lebesgue spaces Lwp(x). We give a condition under which the mentioned modular inequality leads to a norm inequality. Lastly, examples are given to demonstrate our main result, to obtain modular inequalities for some well known operators.
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BibTeX
@misc{madan2026some,
title = {{Some weighted modular inequalities in variable Lebesgue spaces}},
author = {Megha Madan and Arun Pal Singh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09029},
eprint = {2609.09029},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09029},
}
RIS
TY - UNPB
TI - Some weighted modular inequalities in variable Lebesgue spaces
AU - Megha Madan
AU - Arun Pal Singh
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09029
UR - https://arxiv.org/abs/2609.09029
AB - We establish a necessary and sufficient weight condition so that a modular inequality holds for a generalized integral operator T_ϕ on non-negative non-increasing functions in weighted variable Lebesgue spaces L_w^p(x). We give a condition under which the mentioned modular inequality leads to a norm inequality. Lastly, examples are given to demonstrate our main result, to obtain modular inequalities for some well known operators.
ER -