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Mat. Sb. (N.S.), 1983, Volume 122(164), Number 4(12), Pages 511–526 (Mi msb2312)  

This article is cited in 1 scientific paper (total in 1 paper)

The relation between the solid modulus of continuity and the modulus of continuity along the Shilov boundary for analytic functions of several variables

B. Jöricke


Abstract: Let $G\subset\mathbf C^n$ be a bounded doamin and let $\omega$ be a modulus of continuity. This article is devoted to the following problem: which closed sets $S$ with $S\subset\overline G$ possess the property that, for an arbitrary function $f$ belonging to the algebra $A(G)$ of all functions analytic in $G$ and continuous in $\overline G$, the relation
$$ \max_{z,\zeta\in S,|z-\zeta|\leqslant\delta}|f(z)-f(\zeta)|\leqslant\omega(\delta) $$
for all $\delta>0$ implies
$$ \max_{z,\zeta\in\overline G,|z-\zeta|\leqslant\delta}|f(z)-f(\zeta)|\leqslant C\omega(\delta) $$
for all $\delta>0$, where the constant $C$ depends only on $G$ and $S$.
The main result is a theorem which asserts that if $G$ is a regular Weil domain then $S$ can be taken to be the Shilov boundary.
Bibliography: 20 titles.

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English version:
Mathematics of the USSR-Sbornik, 1985, 50:2, 495–511

Bibliographic databases:

UDC: 517.15
MSC: Primary 32A40; Secondary 32E35
Received: 09.02.1982 and 31.05.1983

Citation: B. Jöricke, “The relation between the solid modulus of continuity and the modulus of continuity along the Shilov boundary for analytic functions of several variables”, Mat. Sb. (N.S.), 122(164):4(12) (1983), 511–526; Math. USSR-Sb., 50:2 (1985), 495–511

Citation in format AMSBIB
\Bibitem{Jor83}
\by B.~J\"oricke
\paper The relation between the solid modulus of continuity and the modulus of continuity along the Shilov boundary for analytic functions of several variables
\jour Mat. Sb. (N.S.)
\yr 1983
\vol 122(164)
\issue 4(12)
\pages 511--526
\mathnet{http://mi.mathnet.ru/msb2312}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=725455}
\zmath{https://zbmath.org/?q=an:0541.32002}
\transl
\jour Math. USSR-Sb.
\yr 1985
\vol 50
\issue 2
\pages 495--511
\crossref{https://doi.org/10.1070/SM1985v050n02ABEH002841}


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    This publication is cited in the following articles:
    1. Franzen S., Joricke B., “On Propagation of Boundary Continuity of Holomorphic Functions of Several Variables”, Ann. Scuola Norm. Super. Pisa-Cl. Sci., 7:2 (2008), 271–285  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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