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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

A uniqueness theorem for Riesz potentials


Author: K. A. Izyurov
Translated by: the author
Original publication: Algebra i Analiz, tom 19 (2007), nomer 4.
Journal: St. Petersburg Math. J. 19 (2008), 577-595
MSC (2000): Primary 31A15, 31A20
Published electronically: May 9, 2008
MathSciNet review: 2381935
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Abstract | References | Similar Articles | Additional Information

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}{\vert x\vert^{1-\alpha}}$ at all points of some set of positive length. This result improves that of D. Beliaev and V. Havin.


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Additional 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

DOI: http://dx.doi.org/10.1090/S1061-0022-08-01011-X
PII: S 1061-0022(08)01011-X
Keywords: Riesz potential, uncertainty principle, H\"older condition
Received by editor(s): February 8, 2007
Published electronically: May 9, 2008
Additional Notes: Partially supported by RFBR (grant no. 06-01-00313).
Article copyright: © Copyright 2008 American Mathematical Society