# A Wiener test \`a la Landis for evolutive H\"ormander operators

## TL;DR

This paper establishes a Wiener-type boundary regularity criterion for a broad class of evolutive H"ormander operators, extending classical results to degenerate-parabolic operators with Gaussian bounds.

## Contribution

It introduces a new Wiener criterion for boundary regularity applicable to degenerate-parabolic operators with Gaussian bounds, generalizing Landis's classical result.

## Key findings

- Proves a Wiener-type boundary regularity criterion for evolutive H"ormander operators.
- Extends the criterion to a larger class of degenerate-parabolic operators.
- Uses balayages and Riesz-potentials to characterize boundary regularity.

## Abstract

In this paper we prove a Wiener-type characterization of boundary regularity, in the spirit of a classical result by Landis, for a class of evolutive H\"ormander operators. We actually show the validity of our criterion for a larger class of degenerate-parabolic operators with a fundamental solution satisfying suitable two-sided Gaussian bounds. Our condition is expressed in terms of a series of balayages or, (as it turns out to be) equivalently, Riesz-potentials.