Geometric averaging operators and nonconcentration inequalities

Gressman, Philip T.

doi:10.2140/apde.2022.15.85

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Geometric averaging operators and nonconcentration inequalities

Philip T. Gressman

Vol. 15 (2022), No. 1, 85–122

DOI: 10.2140/apde.2022.15.85

Abstract

This paper is devoted to a systematic study of certain geometric integral inequalities which arise in continuum combinatorial approaches to $L^{p}$ -improving inequalities for Radon-like transforms over polynomial submanifolds of intermediate dimension. The desired inequalities relate to and extend a number of important results in geometric measure theory.

Keywords

geometric measure theory, geometric invariant theory, Radon-like transforms

Mathematical Subject Classification 2010

Primary: 28A75, 44A12

Milestones

Received: 18 June 2019

Revised: 2 June 2020

Accepted: 15 September 2020

Published: 16 March 2022

Authors

Philip T. Gressman
Department of Mathematics University of Pennsylvania Philadelphia, PA United States

Vol. 15, No. 1, 2022