# Geometric averaging operators and nonconcentration inequalities

## TL;DR

This paper systematically studies geometric integral inequalities related to Radon-like transforms over polynomial submanifolds, extending key results in geometric measure theory to improve understanding of $L^p$-inequalities.

## Contribution

It introduces new geometric averaging operators and establishes nonconcentration inequalities, advancing the continuum combinatorial approach to $L^p$-improving inequalities.

## Key findings

- Derived new geometric integral inequalities
- Extended results in geometric measure theory
- Enhanced understanding of Radon-like transforms

## 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.