Geometric averaging operators and nonconcentration inequalities

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.

42 pages

References in corpus (2)

• Universal L^p improving for averages along polynomial curves in low dimensions
• On the Oberlin affine curvature condition

Cited by in corpus (2)

• $L^p$-improving estimates for Radon-like operators and the Kakeya-Brascamp-Lieb inequality
• A restricted $2$-plane transform related to Fourier Restriction for surfaces of codimension $2$