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Arun Pal Singh

Publications and source records attributed to Arun Pal Singh.

4 recordsLinked to original sources
arXiv2026

Some weighted modular inequalities in variable Lebesgue spaces

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.

math.FA↗
arXiv2026

Rubio de Francia Extrapolation Theorem for Quasi non-increasing Sequences

We prove the discrete Rubio de Francia extrapolation theorem for a pair of quasi non-increasing sequences with $\mathcal{QB}_{β, p}$ weight class. Also, a weight characterization of the boundedness of the generalized discrete Hardy averagin19g operator on the class of quasi non-increasing sequences from $l_w^p(\mathbb{Z}^+)$ is proved.

math.FA↗
arXiv2022

Rubio de Francia Extrapolation Theorems for Quasi-Monotone Functions

We prove Rubio de Francia extrapolation results in Lebesgue and grand Lebesgue spaces for quasi monotone functions with $QB_{β,p}$ weights. The extrapolation in Lebesgue spaces with the weight class $QB_{β,\infty}$ has also been investigated. As an application, we characterize the boundedness of the Hardy averaging operator for quasi monotone functions in the grand Lebesgue spaces.

math.FA↗