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Mat. Zametki, 1998, Volume 64, Issue 4, Pages 518–530 (Mi mz1426)  

This article is cited in 3 scientific papers (total in 3 papers)

The boundary behavior of components of polyharmonic functions

K. O. Besov

M. V. Lomonosov Moscow State University

Abstract: We consider the following representation of polyharmonic functions on the unit ball $D^m$:
$$ f=\Phi_0+(1-r^2)\Phi_1+…+(1-r^2)^{n-1}\Phi_{n-1}, $$
where the $\Phi_j$ are harmonic on $D^m$ . We study the relation between uniform boundary properties of $f$ (its smoothness and growth while approaching the boundary) and the same properties of the terms in this representation. The theorems proved in this paper generalize some results obtained by Dolzhenko in the theory of polyanalytic functions.

DOI: https://doi.org/10.4213/mzm1426

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English version:
Mathematical Notes, 1998, 64:4, 450–460

Bibliographic databases:

UDC: 517.575
Received: 26.09.1997

Citation: K. O. Besov, “The boundary behavior of components of polyharmonic functions”, Mat. Zametki, 64:4 (1998), 518–530; Math. Notes, 64:4 (1998), 450–460

Citation in format AMSBIB
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\paper The boundary behavior of components of polyharmonic functions
\jour Mat. Zametki
\yr 1998
\vol 64
\issue 4
\pages 518--530
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\crossref{https://doi.org/10.4213/mzm1426}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1687236}
\zmath{https://zbmath.org/?q=an:0939.31007}
\transl
\jour Math. Notes
\yr 1998
\vol 64
\issue 4
\pages 450--460
\crossref{https://doi.org/10.1007/BF02314625}
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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. K. O. Besov, “On the Nikol'skii Classes of Polyharmonic Functions”, Proc. Steklov Inst. Math., 227 (1999), 37–49  mathnet  mathscinet  zmath
    2. V. V. Karachik, “Integralnye tozhdestva na sfere dlya normalnykh proizvodnykh poligarmonicheskikh funktsii”, Sib. elektron. matem. izv., 14 (2017), 533–551  mathnet  crossref  mathscinet  zmath
    3. M. Ya. Mazalov, “On the existence of angular boundary values for polyharmonic functions in the unit ball”, J. Math. Sci. (N. Y.), 234:3 (2018), 362–368  mathnet  crossref
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