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The Green function with pole at infinity applied to the study of the elliptic measure

Joseph Feneuil

Vol. 16 (2023), No. 2, 545–570
Abstract

In +d+1 or in n d (d < n 1), we study the Green function with pole at infinity defined for instance by David, Engelstein, and Mayboroda. In two cases, we deduce the equivalence between the elliptic measure and the Lebesgue measure on d. We further prove the A-absolute continuity of the elliptic measure for operators that can be related to the two previous cases via Carleson measures, extending the range of operators for which the A-absolute continuity of the elliptic measure is known.

Keywords
Green function with pole at infinity, elliptic measure, $A_{\infty}$-absolute continuity
Mathematical Subject Classification
Primary: 35J25, 42B37
Milestones
Received: 22 October 2020
Revised: 26 May 2021
Accepted: 15 July 2021
Published: 3 May 2023
Authors
Joseph Feneuil
Laboratoire de mathématiques d’Orsay
Université Paris-Saclay
Orsay
France

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