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Proceedings of the American Mathematical Society

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Sharp-edged square functions


Author: Michael Wilson
Journal: Proc. Amer. Math. Soc. 147 (2019), 2405-2412
MSC (2010): Primary 42B25; Secondary 42C15, 42C40
DOI: https://doi.org/10.1090/proc/14174
Published electronically: March 1, 2019
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Abstract: We prove $ L^2\to L^2$ boundedness for a type of intrinsic square function in which the constituent kernels (`` wavelets'') are not assumed to have pointwise smoothness or carefully placed discontinuities. Aside from the usual assumptions of cancellation and bounded supports, we ask only that our functions be of uniformly bounded variation on lines parallel to the coordinate axes.


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Additional Information

Michael Wilson
Affiliation: Department of Mathematics, University of Vermont, Burlington, Vermont 05405

DOI: https://doi.org/10.1090/proc/14174
Keywords: Littlewood--Paley theory, intrinsic square function, almost-orthogonality
Received by editor(s): August 4, 2017
Received by editor(s) in revised form: February 15, 2018
Published electronically: March 1, 2019
Communicated by: Svitlana Mayboroda
Article copyright: © Copyright 2019 American Mathematical Society