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 Mat. Sb., 2008, Volume 199, Number 1, Pages 47–66 (Mi msb3783)

Precise characterizations of admissible rate of decrease of a non-trivial function with zero ball means

O. A. Ochakovskaya

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences

Abstract: Precise characterizations of an admissible rate of decrease of a non-trivial function having zero integrals over all balls of fixed radius are established. The case of an essentially anisotropic behaviour of the function at infinity is considered for the first time. In particular, the function is even allowed to grow exponentially in one variable, which is compensated in a certain sense by its rapid decrease in other variables.
Bibliography: 17 titles.

DOI: https://doi.org/10.4213/sm3783

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English version:
Sbornik: Mathematics, 2008, 199:1, 45–65

Bibliographic databases:

UDC: 517.444
MSC: Primary 26B15, 43A85; Secondary 53C65
Received: 19.10.2006 and 12.07.2007

Citation: O. A. Ochakovskaya, “Precise characterizations of admissible rate of decrease of a non-trivial function with zero ball means”, Mat. Sb., 199:1 (2008), 47–66; Sb. Math., 199:1 (2008), 45–65

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb3783
• https://doi.org/10.4213/sm3783
• http://mi.mathnet.ru/eng/msb/v199/i1/p47

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Ochakovskaya O.A., “On the injectivity of the Pompeiu transform for integral ball means”, Ukr. Math. J., 63:3 (2011), 416–424
2. Volchkov V.V., Volchkov Vit.V., “Analogues of the Liouville theorem for solutions of the twisted convolution equation”, Dokl. Math., 83:2 (2011), 197–200
3. Ochakovskaya O.A., “The boundary behavior of functions with vanishing integrals over hyperbolic disks”, Dokl. Math., 86:1 (2012), 534–536
4. O. A. Ochakovskaya, “Theorems on ball mean values for solutions of the Helmholtz equation on unbounded domains”, Izv. Math., 76:2 (2012), 365–374
5. V. V. Volchkov, Vit. V. Volchkov, “Behaviour at infinity of solutions of twisted convolution equations”, Izv. Math., 76:1 (2012), 79–93
6. Ochakovskaya O.A., “Injectivity classes of the Pompeiu transformation”, Ukr. Math. J., 64:12 (2013), 1893–1902
7. O. A. Ochakovskaya, “Boundary uniqueness theorems for functions whose integrals over hyperbolic discs vanish”, Sb. Math., 204:2 (2013), 264–279
8. O. A. Ochakovskaya, “Radial majorants of functions with zero integrals over balls of a fixed radius”, Izv. Math., 78:3 (2014), 580–595
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