On almost everywhere convergence of strong arithmetic means of Fourier series
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Abstract:
This article establishes a real-variable argument for Zygmund’s theorem on almost everywhere convergence of strong arithmetic means of partial sums of Fourier series on $\mathbb {T}$, up to passing to a subsequence. Our approach extends to, among other cases, functions that are defined on $\mathbb {T}^d$, which allows us to establish an analogue of Zygmund’s theorem in higher dimensions.References
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Additional Information
- Bobby Wilson
- Affiliation: Department of Mathematics, The University of Chicago, 5734 South University Avenue, Chicago, Illinois 60615
- Received by editor(s): May 8, 2013
- Received by editor(s) in revised form: October 1, 2013
- Published electronically: September 5, 2014
- Additional Notes: This is in partial fulfillment of the author’s requirements for the Doctor of Philosophy degree in Mathematics at the University of Chicago
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 367 (2015), 1467-1500
- MSC (2010): Primary 42A20, 42A24
- DOI: https://doi.org/10.1090/S0002-9947-2014-06297-1
- MathSciNet review: 3280051