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Mat. Zametki, 1998, Volume 63, Issue 6, Pages 821–834 (Mi mz1352)  

This article is cited in 8 scientific papers (total in 8 papers)

On boundary properties of the components of polyharmonic functions

E. P. Dolzhenko

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The following two classes of functions are introduced for $p\ge0$: the class $CU^p(G)$ of uniformly continuous functions of order $p$ in a domain $G\subset\mathbb C$, and the class $\mathfrak M^p(G)$ of functions of the boundedness of order $p$ in $G$. Criterions are established for an $n$-analytic function to belong to each of these classes.

DOI: https://doi.org/10.4213/mzm1352

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English version:
Mathematical Notes, 1998, 63:6, 724–735

Bibliographic databases:

UDC: 517.5
Received: 28.10.1996

Citation: E. P. Dolzhenko, “On boundary properties of the components of polyharmonic functions”, Mat. Zametki, 63:6 (1998), 821–834; Math. Notes, 63:6 (1998), 724–735

Citation in format AMSBIB
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\paper On boundary properties of the components of polyharmonic functions
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\vol 63
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\pages 821--834
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\jour Math. Notes
\yr 1998
\vol 63
\issue 6
\pages 724--735
\crossref{https://doi.org/10.1007/BF02312765}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. O. Besov, “The boundary behavior of components of polyharmonic functions”, Math. Notes, 64:4 (1998), 450–460  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. K. Ramazanov, “Representation of the space of polyanalytic functions as the direct sum of orthogonal subspaces. Application to rational approximations”, Math. Notes, 66:5 (1999), 613–627  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. K. O. Besov, “On the Nikol'skii Classes of Polyharmonic Functions”, Proc. Steklov Inst. Math., 227 (1999), 37–49  mathnet  mathscinet  zmath
    4. A.-R. K. Ramazanov, “On the Structure of Spaces of Polyanalytic Functions”, Math. Notes, 72:5 (2002), 692–704  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. E. P. Dolzhenko, V. I. Danchenko, “On the Boundary Properties of Solutions to the Generalized Cauchy–Riemann Equation”, Proc. Steklov Inst. Math., 236 (2002), 132–142  mathnet  mathscinet  zmath
    6. A. K. Ramazanov, “Estimate of the Norm of a Polyanalytic Function via the Norm of Its Polyharmonic Component”, Math. Notes, 75:4 (2004), 568–573  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. M. Ya. Mazalov, P. V. Paramonov, K. Yu. Fedorovskiy, “Conditions for $C^m$-approximability of functions by solutions of elliptic equations”, Russian Math. Surveys, 67:6 (2012), 1023–1068  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. 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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