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Proceedings of the American Mathematical Society

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Another counterexample to Zygmund's conjecture


Author: Guillermo Rey
Journal: Proc. Amer. Math. Soc. 148 (2020), 5269-5275
MSC (2010): Primary 42B25
DOI: https://doi.org/10.1090/proc/15222
Published electronically: September 24, 2020
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Abstract: We present a simple dyadic construction that yields a new counterexample to Zygmund's conjecture in differentiation of integrals. Our result recovers Soria's classical results in dimensions three and four, through a different construction, and gives new ones in all other dimensions.


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Additional Information

Guillermo Rey
Affiliation: Citadel, 131 S Dearborn St, Chicago, Illinois 60603
MR Author ID: 1050866
Email: guillermo.reyley@gmail.com

DOI: https://doi.org/10.1090/proc/15222
Received by editor(s): April 4, 2020
Received by editor(s) in revised form: May 25, 2020
Published electronically: September 24, 2020
Communicated by: Dmitriy Bilyk
Article copyright: © Copyright 2020 American Mathematical Society