Rearrangements and infimum convolutions
Devraj Duggal, James Melbourne, and Cyril Roberto
TL;DR
This paper introduces a general comparison framework for inf convolution operators linked to rearrangement, leading to new comparison results for Laplace and polar transforms, and simplifying proofs of known inequalities.
Contribution
It develops a broad comparison result for inf convolution operators and applies it to derive new and simplified inequalities involving rearrangements and PDEs.
Findings
Comparison results for Laplace and polar transforms under rearrangement
Simplified proofs of the functional Blaschke Santaló inequality
New comparison result for certain parabolic PDEs
Abstract
We develop a general comparison result for inf convolution operators related to rearrangement. As a consequence we derive comparison results under spherically symmetric rearrangement for Laplace and polar transforms. As a by product we simplify existing proofs related to the functional Blaschke Santalo inequality of Keith Ball and derive a comparison result for some parabolic PDE.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Harmonic Analysis Research · Mathematical Analysis and Transform Methods