dc.contributor.author
Bortz, S.
dc.contributor.author
Egert, M.
dc.contributor.author
Saari, O.
dc.date.accessioned
2025-06-16T11:23:55Z
dc.date.available
2025-06-16T11:23:55Z
dc.date.issued
2025-08-01
dc.identifier.uri
http://hdl.handle.net/2072/484449
dc.description.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.
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dc.description.sponsorship
This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany\u2019s Excellence Strategy \u2013 EXC-2047/1 \u2013 390685813 and CRC 1060, by the ANR project RAGE ANR-18-CE40-0012 and by \u2018Verein von Freunden der Technischen Universit\u00E4t zu Darmstadt e.V.\u2019. The first author would like to thank Tatiana Toro and Zihui Zhao for some helpful comments about the paper.; Funding text 2: This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy \u2013 EXC-2047/1 \u2013 390685813 and CRC 1060, by the ANR project RAGE ANR-18-CE40-0012 and by \u2018Verein von Freunden der Technischen Universit\u00E4t zu Darmstadt e.V.\u2019. The third author was supported by Generalitat de Catalunya through the grant 2021-SGR-00087 and by the Spanish State Research Agency MCIN/AEI/10.13039/501100011033, Next Generation EU and by ERDF \u201CA way of making Europe\u201D through the grants RYC2021-032950-I, RED2022-134784-T, PID2021-123903NB-I00 and the Severo Ochoa and Maria de Maeztu Program for Centers and Units of Excellence in R&D, grant number CEX2020-001084-M. The first author would like to thank Tatiana Toro and Zihui Zhao for some helpful comments about the paper.
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dc.format.extent
11 p.
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dc.relation.ispartof
Nonlinear Analysis, Theory, Methods and Applications
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dc.rights
Attribution 4.0 International
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Boundary value problems
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dc.subject.other
Carleson measures
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dc.subject.other
Elliptic measure
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dc.subject.other
Muckenhoupt weights
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dc.subject.other
Perturabations
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dc.title
Carleson conditions for weights: The quantitative small constant case
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dc.type
info:eu-repo/semantics/article
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dc.description.version
info:eu-repo/semantics/publishedVersion
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dc.identifier.doi
10.1016/j.na.2025.113802
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dc.rights.accessLevel
info:eu-repo/semantics/openAccess
