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Mat. Sb. (N.S.), 1973, Volume 92(134), Number 1(9), Pages 34–54 (Mi msb3330)  

This article is cited in 6 scientific papers (total in 6 papers)

Equivalent norms in spaces of entire functions

V. È. Katsnelson


Abstract: It is shown that if $E\subset\mathbf R^n$ is relatively dense with respect to Lebesgue mesure and $p\in(0,\infty)$, then for any entire function $f(z)$ of $n$ complex variables and of exponential type not exceeding $\sigma$ the inequality
$$ \int_E|f(x)|^p dx_1…dx_n\geqslant c\int_{\mathbf R^n}|f(x)|^p dx_1…dx_n $$
is satisfied, where $c$ is a constant depending only on $\sigma$, $L$, $\delta$ and $p$, but not on $f(z)$, and the integrals on both sides of the inequality converge or diverge simultaneously.
Bibliography: 11 titles.

Full text: PDF file (1650 kB)
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English version:
Mathematics of the USSR-Sbornik, 1973, 21:1, 33–55

Bibliographic databases:

UDC: 517.535+519.53
MSC: Primary 31B05, 32F05, 46E15; Secondary 30A44
Received: 06.09.1972

Citation: V. È. Katsnelson, “Equivalent norms in spaces of entire functions”, Mat. Sb. (N.S.), 92(134):1(9) (1973), 34–54; Math. USSR-Sb., 21:1 (1973), 33–55

Citation in format AMSBIB
\Bibitem{Kat73}
\by V.~\`E.~Katsnelson
\paper Equivalent norms in spaces of entire functions
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 92(134)
\issue 1(9)
\pages 34--54
\mathnet{http://mi.mathnet.ru/msb3330}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=338406}
\zmath{https://zbmath.org/?q=an:0288.46024}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 21
\issue 1
\pages 33--55
\crossref{https://doi.org/10.1070/SM1973v021n01ABEH002004}


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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. A. L. Vol'berg, “The comparative strength of integral norms on subspaces of pseudo-extendable functions in the space $H^p$”, Russian Math. Surveys, 36:6 (1981), 203–204  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. John P. Nolan, Zachariah Sinkala, “Equivalent norms on analytic subspaces of LP”, Journal of Mathematical Analysis and Applications, 126:1 (1987), 238  crossref  mathscinet  zmath
    3. V. N. Logvinenko, “Boundedness conditions for entire functions of exponential type interior to the hyperoctant $\mathbf R_+^n$”, Math. USSR-Izv., 34:3 (1990), 663–676  mathnet  crossref  mathscinet  zmath
    4. V. B. Sherstyukov, “On a Problem of Leont'ev and Representing Systems of Exponentials”, Math. Notes, 74:2 (2003), 286–298  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Michael I. Ganzburg, Paul Nevai, Tamás Erdélyi, “M. Riesz-Schur-type inequalities for entire functions of exponential type”, Sb. Math., 206:1 (2015), 24–32  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. V. B. Sherstyukov, “Distribution of the zeros of canonical products and weighted condensation index”, Sb. Math., 206:9 (2015), 1299–1339  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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