Work

Carleson conditions for weights: The quantitative small constant case

Year: 2025

Type: article

Abstract: We investigate the small constant case of a characterization of A ∞ weights due to Fefferman, Kenig and Pipher. In their work, Fefferman, Kenig and Pipher bound the logarithm of the A ∞ constant by the Carleson norm of a measure built out of the heat extension, up to a multiplicative and additive constant (as well as the converse). We prove, qualitatively, that when one of these quantities is small, then so is the other. In fact, we show that these quantities are bounded by a constant times the square root of the other, provided at least one of them is sufficiently small. We also give an application of our result to the study of elliptic measures associated to elliptic operators with coefficients satisfying the “Dahlberg–Kenig–Pipher” condition.

Source: Nonlinear Analysis

DOI: 10.1016/j.na.2025.113802

Authors: Simon Bortz, Moritz Egert, Olli Saari

Institutions: University of Alabama, Technische Universität Darmstadt, Centre de Recerca Matemàtica, Universitat Politècnica de Catalunya

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,690