Sharp mixed Ap-A∞ estimates for sparse operators on filtered and nonhomogeneous measure spaces
Abstract
We prove mixed Ap-A∞ estimates for sparse operators in two non-doubling settings. In the first setting, we consider sparse operators defined using stopping times in continuous time. We obtain both strong- and weak-type bounds with the same powers of the weight characteristics as in the classical setting. Some of our weak-type bounds are even new for the dyadic filtration on ℝd and, in particular, imply a sharp weak-type (2,2) estimate for Rubio de Francia square functions, solving a problem left open by Garg, Roncal and Shrivastava [J. Geom. Anal., 31:748-771, 2021]. In the second setting, we consider dyadic sparse forms in which distinct cubes may interact, provided their dyadic distance is bounded. We obtain strong-type bounds with the same powers of the weight characteristics as in the classical setting. As a one-dimensional application, we obtain strong-type bounds for Haar shifts over balanced non-doubling measures, answering a quantitative question posed by Conde-Alonso, Pipher, and Wagner [Math. Ann., 391:2209-2253, 2025].
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BibTeX
@misc{goncalves2026sharp,
title = {{Sharp mixed $A_p$-$A_\infty$ estimates for sparse operators on filtered and nonhomogeneous measure spaces}},
author = {Francisco Gonçalves and Emiel Lorist},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20531},
eprint = {2609.20531},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20531},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sharp mixed A_p-A_∞ estimates for sparse operators on filtered and nonhomogeneous measure spaces
AU - Francisco Gonçalves
AU - Emiel Lorist
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20531
UR - https://arxiv.org/abs/2609.20531
AB - We prove mixed A_p-A_∞ estimates for sparse operators in two non-doubling settings. In the first setting, we consider sparse operators defined using stopping times in continuous time. We obtain both strong- and weak-type bounds with the same powers of the weight characteristics as in the classical setting. Some of our weak-type bounds are even new for the dyadic filtration on ℝ^d and, in particular, imply a sharp weak-type (2,2) estimate for Rubio de Francia square functions, solving a problem left open by Garg, Roncal and Shrivastava [J. Geom. Anal., 31:748-771, 2021]. In the second setting, we consider dyadic sparse forms in which distinct cubes may interact, provided their dyadic distance is bounded. We obtain strong-type bounds with the same powers of the weight characteristics as in the classical setting. As a one-dimensional application, we obtain strong-type bounds for Haar shifts over balanced non-doubling measures, answering a quantitative question posed by Conde-Alonso, Pipher, and Wagner [Math. Ann., 391:2209-2253, 2025].
ER -