Inequalities for Pairs of Measure Spaces and Applications
P. D. Johnson, R. N. Mohapatra, Shankhadeep Mondal

TL;DR
This paper introduces a generalized Jensen-type inequality for pairs of measure spaces, extending classical inequalities like Hölder's and Minkowski, with applications to various mathematical and probabilistic models.
Contribution
It establishes a broad, unifying inequality framework that encompasses and extends classical measure inequalities, with sharp equality conditions and multiple applications.
Findings
Unified Jensen-type inequality for measure spaces
Extensions of classical inequalities with sharp equality conditions
Applications to convolution operators and probabilistic models
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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Taxonomy
TopicsMathematical Inequalities and Applications · Optimization and Variational Analysis · Contact Mechanics and Variational Inequalities
