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arXiv · 2609.09029

Some weighted modular inequalities in variable Lebesgue spaces

Megha Madan·Arun Pal Singh
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Abstract

We establish a necessary and sufficient weight condition so that a modular inequality holds for a generalized integral operator $T_\phi$ 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.

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Megha Madan, Arun Pal Singh. 2026-09-08. Some weighted modular inequalities in variable Lebesgue spaces. https://arxiv.org/abs/2609.09029

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