Characterization of weakly porous sets via dyadic coverings

TL;DR

This paper characterizes weakly porous sets in Euclidean spaces using dyadic coverings and establishes a Carleson embedding inequality for these sets, advancing the understanding of their geometric and measure-theoretic properties.

Contribution

It provides a new precise characterization of weakly porous sets via dyadic coverings and proves a Carleson embedding inequality specific to porous sets.

Findings

Dyadic covering characterization of weakly porous sets

Proof of Carleson embedding inequality for porous sets

Enhanced understanding of porous set structure in Euclidean spaces

Abstract

We consider the class of weakly porous sets in Euclidean spaces. As our main goal, we give a precise characterization in terms of dyadic covering of these sets. Also, we obtain the Carleson embedding inequality for porous sets.