Vol. 15, No. 1, 2022

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Geometric averaging operators and nonconcentration inequalities

Philip T. Gressman

Vol. 15 (2022), No. 1, 85–122
Abstract

This paper is devoted to a systematic study of certain geometric integral inequalities which arise in continuum combinatorial approaches to Lp-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.

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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