#### 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 ${L}^{p}$-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