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arXiv · 2603.06241

Inequalities for Pairs of Measure Spaces and Applications

P. D. Johnson·R. N. Mohapatra·Shankhadeep Mondal
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Abstract

We study a family of inequalities on pairs of measure spaces involving functions defined on product domains. Our main result establishes a Jensen-type inequality under a general product-measure framework, extending classical inequalities such as H\"older's and Minkowski's as special cases. The inequality admits sharp characterizations of equality and yields quantitative, variational, and probabilistic refinements under additional convexity assumptions. Several corollaries illustrate power-mean, entropy-type, and erasure-robust inequalities, as well as applications to convolution-type operators and weighted discrete models.

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P. D. Johnson, R. N. Mohapatra, Shankhadeep Mondal. 2026-03-06. Inequalities for Pairs of Measure Spaces and Applications. https://arxiv.org/abs/2603.06241

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