Arkiv för Matematik

  • Ark. Mat.
  • Volume 39, Number 2 (2001), 223-243.

On the uncertainty principle for M. Riesz potentials

Dmitri B. Beliaev and Victor P. Havin

Full-text: Open access

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Research supported in part by RFFI, grant N 99-01-00720 and NSERC.

Article information

Source
Ark. Mat., Volume 39, Number 2 (2001), 223-243.

Dates
Received: 17 April 2000
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898730

Digital Object Identifier
doi:10.1007/BF02384555

Mathematical Reviews number (MathSciNet)
MR1861059

Zentralblatt MATH identifier
1037.42016

Rights
2001 © Institut Mittag-Leffler

Citation

Beliaev, Dmitri B.; Havin, Victor P. On the uncertainty principle for M. Riesz potentials. Ark. Mat. 39 (2001), no. 2, 223--243. doi:10.1007/BF02384555. https://projecteuclid.org/euclid.afm/1485898730


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References

  • Aleksandrov, A. B. and Kargaev P. P., Hardy classes of functions harmonic in the upper halfspace, Algebra i Analiz 5:2 (1993), 1–73 (Russian). English transl.: St. Petersburg Math. J. 5 (1994), 229–286.
  • Binder, I., A theorem on correction of gradients of harmonic functions, Algebra i Analiz 5:2 (1993), 91–107 (Russian). English transl.: St. Petersburg Math. J. 5 (1994), 301–315.
  • Bourgain, J. and Wolff, T., A remark on gradients of harmonic functions in dimension ≥3, Colloq. Math. 60/61 (1990), 253–260.
  • Goluzina, M. G., On a uniqueness theorem, Vestnik Leningrad. Univ. Mat. Mekh. Astronom. 1987:1 (1987), 109–111, 127 (Russian).
  • Havin, V., The uncertainty principle for one-dimensional Riesz potentials, Doklady Akad. Nauk SSSR 264 (1982), 559–563 (Russian). English transl.: Soviet Math. Dokl. 25 (1982), 694–698.
  • Havin, V. and Jöricke, B., The Uncertainty Principle in Harmonic Analysis, Springer-Verlag, Berlin, 1994.
  • Havin, V. and Maz’ya, V., On solutions of the Cauchy problem for the Laplace equation (uniqueness, normality, approximation), Trudy Moskov. Mat. Obshch. 30 (1974), 61–114 (Russian). English transl.: Trans. Moscow Math. Soc. 30 (1974), 65–117.
  • Jöricke, B. and Havin, V., The uncertainty principle for operators commuting with the shift, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 113 (1982), 97–134, 265.
  • Kislyakov, S. V., A new correction theorem, Izv. Akad. Nauk SSSR Ser. Mat. 48:2 (1984), 305–330 (Russian). English transl.: Math. USSR-Izv. 24 (1985), 283–306.
  • Riesz, M., Intégrales de Riemann-Liouville et potentiels, Acta Sci. Math. (Szeged) 9 (1938), 1–42.
  • Samko, S. G., Kilbas, A. A. and Marichev, O. I., Integrals and Derivatives of Fractional Order and Some of Their Applications, Nauka i tekhnika, Minsk, 1987.
  • Wolff, T., Counterexamples with harmonic gradients in R3, in Essays on Fourier Analysis in Honor of Elias M. Stein (Princeton, N. J. 1991) (Fefferman, C., Fefferman, R. and Wainger, S., eds.), pp. 321–384, Princeton Univ. Press, Princeton, N. J., 1995.