Another counterexample to Zygmund’s conjecture

Rey, Guillermo

doi:10.1090/proc/15222

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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