Inequalities for Pairs of Measure Spaces and Applications
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908870246400000 |
|---|---|
| author | Johnson, P. D. Mohapatra, R. N. Mondal, Shankhadeep |
| author_facet | Johnson, P. D. Mohapatra, R. N. Mondal, Shankhadeep |
| contents | 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 Hölder'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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06241 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inequalities for Pairs of Measure Spaces and Applications Johnson, P. D. Mohapatra, R. N. Mondal, Shankhadeep Functional Analysis 26D15, 42C15, 46E30, 05C50, 60E15 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 Hölder'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. |
| title | Inequalities for Pairs of Measure Spaces and Applications |
| topic | Functional Analysis 26D15, 42C15, 46E30, 05C50, 60E15 |
| url | https://arxiv.org/abs/2603.06241 |