Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Madan, Megha, Singh, Arun Pal
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212050597