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A uniqueness theorem for Riesz potentials
Author(s):
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
Posted:
May 9, 2008
MathSciNet review:
2381935
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Additional information
Abstract:
The existence is proved of a nonzero Hölder function  that vanishes together with its M. Riesz potential  at all points of some set of positive length. This result improves that of D. Beliaev and V. Havin.
References:
-
- 1.
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- 2.
- D. B. Beliaev and V. P. Havin, On the uncertainty principle for M. Riesz potentials, Ark. Mat. 39 (2001), 229-243. MR 1861059 (2003a:31002)
- 3.
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- 4.
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- V. P. Havin, The uncertainty principle for one-dimensional Riesz potentials, Dokl. Akad. Nauk SSSR 264 (1982), no. 3, 559-563; English transl., Soviet Math. Dokl. 25 (1982), no. 3, 694-698. MR 0659763 (84j:31002)
- 6.
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 , Essays on Fourier Analysis in Honor of Elias M. Stein (Princeton, NJ., 1991) (C. Fefferman, R. Fefferman, and S. Wainger, eds.), Princeton Math. Ser., vol. 42, Princeton Univ. Press, Princeton, NJ, 1995, pp. 321-384. MR 1315554 (95m:31010) - 8.
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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:
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):
8/FEB/2007
Posted:
May 9, 2008
Additional Notes:
Partially supported by RFBR (grant no.~06-01-00313).
Copyright of article:
Copyright
2008,
American Mathematical Society
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