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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A hierarchy of thin sets related to the boundedness of trigonometric series


Author: Peter Elias
Journal: Proc. Amer. Math. Soc. 128 (2000), 3341-3347
MSC (2000): Primary 43A46; Secondary 42A05, 42A32
Published electronically: May 11, 2000
MathSciNet review: 1707515
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Abstract:

We study the family  $\mathcal{B}_0$ of the sets on which some series of the form $\sum_{k\in{\Bbb N}}\left\vert\sin\pi n_kx\right\vert$ is uniformly bounded. We show that the families  $\mathcal{B}_0^c$ of all sets admitting the boundary $c$ form a hierarchy which is incontinuous with respect to the operations of intersection and union.


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Additional Information

Peter Elias
Affiliation: Mathematical Institute, Slovak Academy of Sciences, Jesenná 5, 041 54 Košice, Slovakia
Email: elias@kosice.upjs.sk

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05560-X
PII: S 0002-9939(00)05560-X
Keywords: Trigonometric thin sets, N$_0$-sets, B$_0$-sets, uniform boundedness
Received by editor(s): January 12, 1999
Published electronically: May 11, 2000
Additional Notes: This work was supported by grant 2/4034/97 of Slovak Grant Agency VEGA. The research was partly done when the author was visiting the Mathematical Institute of the University in Bonn with financial support by the Graduiertenkolleg.
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2000 American Mathematical Society