Abstract
We prove a local Tb theorem for square functions, in which we assume L p control of the pseudo-accretive system, with p>1 extending the work of S. Hofmann to domains with Ahlfors–David regular boundaries.
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Acknowledgements
We would like to thank Steve Hofmann for suggesting this problem to us, for our discussions with him that illuminated the dyadic analysis part of the paper, and in general, for his constant support. The second named author has benefited from a two-year Sophie Germain International post-doctoral scholarship in Fondation de Mathématiques Jacques Hadamard (FMJH) and would like to thank Université Paris-Sud 11, Orsay, for its hospitality. This work started when the second named author was a research assistant under Steve Hofmann in the Department of Mathematics at the University of Missouri, Columbia.
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Communicated by Michael Lacey.
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Grau de la Herran, A., Mourgoglou, M. A Local Tb Theorem for Square Functions in Domains with Ahlfors–David Regular Boundaries. J Geom Anal 24, 1619–1640 (2014). https://doi.org/10.1007/s12220-013-9388-7
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DOI: https://doi.org/10.1007/s12220-013-9388-7