A uniqueness theorem for Riesz potentials
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K. A. Izyurov
Translated by: the author - St. Petersburg Math. J. 19 (2008), 577-595
- DOI: https://doi.org/10.1090/S1061-0022-08-01011-X
- Published electronically: May 9, 2008
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Abstract:
The existence is proved of a nonzero Hölder function $f:\mathbb {R}\rightarrow \mathbb {R}$ that vanishes together with its M. Riesz potential $f\ast \frac {1}{|x|^{1-\alpha }}$ at all points of some set of positive length. This result improves that of D. Beliaev and V. Havin.References
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Bibliographic Information
- K. A. Izyurov
- Affiliation: Mathematics and Mechanics Department, St. Petersburg State University, Universitetskii Prospekt 28, Staryi Peterhof, St. Petersburg 198504, Russia
- Email: k.izyurov@gmail.com
- Received by editor(s): February 8, 2007
- Published electronically: May 9, 2008
- Additional Notes: Partially supported by RFBR (grant no. 06-01-00313).
- © Copyright 2008 American Mathematical Society
- Journal: St. Petersburg Math. J. 19 (2008), 577-595
- MSC (2000): Primary 31A15, 31A20
- DOI: https://doi.org/10.1090/S1061-0022-08-01011-X
- MathSciNet review: 2381935