A hierarchy of thin sets related to the boundedness of trigonometric series
HTML articles powered by AMS MathViewer
- by Peter Eliaš PDF
- Proc. Amer. Math. Soc. 128 (2000), 3341-3347 Request permission
Abstract:
We study the family $\mathcal {B}_0$ of the sets on which some series of the form $\sum _{k\in \mathbb {N}}\left |\sin \pi n_kx\right |$ 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.References
- P. Hebroni, Sur les inverses des éléments dérivables dans un anneau abstrait, C. R. Acad. Sci. Paris 209 (1939), 285–287 (French). MR 14
- Lev Bukovský, Natasha N. Kholshchevnikova, and Miroslav Repický, Thin sets of harmonic analysis and infinite combinatorics, Real Anal. Exchange 20 (1994/95), no. 2, 454–509. MR 1348075, DOI 10.2307/44152535
- Peter Eliaš, A classification of trigonometrical thin sets and their interrelations, Proc. Amer. Math. Soc. 125 (1997), no. 4, 1111–1121. MR 1363456, DOI 10.1090/S0002-9939-97-03661-7
Additional Information
- Peter Eliaš
- Affiliation: Mathematical Institute, Slovak Academy of Sciences, Jesenná 5, 041 54 Košice, Slovakia
- Email: elias@kosice.upjs.sk
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3341-3347
- MSC (2000): Primary 43A46; Secondary 42A05, 42A32
- DOI: https://doi.org/10.1090/S0002-9939-00-05560-X
- MathSciNet review: 1707515