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Uspekhi Mat. Nauk, 1970, Volume 25, Issue 6(156), Pages 129–191 (Mi umn5429)  

This article is cited in 17 scientific papers (total in 18 papers)

Resonance theorems and superlinear operators

E. M. Nikishin


Abstract: This article is concerned with problems of the metrical theory of functions. We establish criteria for systems of measurable functions to be systems of convergence in measure, systems of convergence almost everywhere, etc. The exposition is based on a unified method, using superlinear operators.

Full text: PDF file (5091 kB)

English version:
Russian Mathematical Surveys, 1970, 25:6, 125–187

Bibliographic databases:

UDC: 517.43
MSC: 47B65, 28A20, 28A33, 42C20, 42A20
Received: 16.02.1970

Citation: E. M. Nikishin, “Resonance theorems and superlinear operators”, Uspekhi Mat. Nauk, 25:6(156) (1970), 129–191; Russian Math. Surveys, 25:6 (1970), 125–187

Citation in format AMSBIB
\Bibitem{Nik70}
\by E.~M.~Nikishin
\paper Resonance theorems and superlinear operators
\jour Uspekhi Mat. Nauk
\yr 1970
\vol 25
\issue 6(156)
\pages 129--191
\mathnet{http://mi.mathnet.ru/umn5429}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=296584}
\zmath{https://zbmath.org/?q=an:0222.47024|0226.47042}
\transl
\jour Russian Math. Surveys
\yr 1970
\vol 25
\issue 6
\pages 125--187
\crossref{https://doi.org/10.1070/RM1970v025n06ABEH001270}


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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. S. S. Kutateladze, A. M. Rubinov, “Minkowski duality and its applications”, Russian Math. Surveys, 27:3 (1972), 137–191  mathnet  crossref  mathscinet  zmath
    2. E. M. Nikishin, “A resonance theorem and series in eigenfunctions of the Laplacian”, Math. USSR-Izv., 6:4 (1972), 788–806  mathnet  crossref  mathscinet  zmath
    3. L. V. Zhizhiashvili, “Some problems in the theory of simple and multiple trigonometric and orthogonal series”, Russian Math. Surveys, 28:2 (1973), 65–127  mathnet  crossref  mathscinet  zmath
    4. B. S. Kashin, “On unconditional convergence in the space $L_1$”, Math. USSR-Sb., 23:4 (1974), 509–519  mathnet  crossref  mathscinet  zmath
    5. A. M. Rubinov, “Sublinear operators and their applications”, Russian Math. Surveys, 32:4 (1977), 115–175  mathnet  crossref  mathscinet  zmath
    6. D. V. Pecherskii, “A theorem on projections of rearranged series with terms in $L_p$”, Math. USSR-Izv., 11:1 (1977), 193–204  mathnet  crossref  mathscinet  zmath
    7. A. V. Bukhvalov, “Application of methods of the theory of order-bounded operators to the theory of operators in $L^p$-spaces”, Russian Math. Surveys, 38:6 (1983), 43–98  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. E. M. Semënov, A. M. Shteinberg, “Otsenki norm operatornykh blokov v banakhovykh reshetkakh”, Matem. sb., 126(168):3 (1985), 327–343  mathnet  mathscinet  zmath; E. M. Semenov, A. M. Shteinberg, “Norm estimates of operator blocks in Banach lattices”, Math. USSR-Sb., 54:2 (1986), 317–333  crossref
    9. A. G. Vitushkin, A. A. Gonchar, B. S. Kashin, A. I. Kostrikin, S. M. Nikol'skii, S. P. Novikov, P. L. Ul'yanov, L. D. Faddeev, “Evgenii Mikhailovich Nikishin (obituary)”, Russian Math. Surveys, 42:5 (1987), 153–160  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. P. L. Ul'yanov, “Development of D. E. Men'shov's results in the theory of orthogonal series”, Russian Math. Surveys, 47:5 (1992), 49–70  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. Kozlov A., “Multifunctionality and Interchangeability in Operations of the Thoracic Legs of the Gaddisworms Phryganea-Grandis (Insecta, Trichoptera)”, Zool. Zhurnal, 71:11 (1992), 61–66  isi
    12. S. A. Pichugov, “Posledovatelnosti ogranichennykh po mere operatorov”, Matem. sb., 185:1 (1994), 43–72  mathnet  mathscinet  zmath; S. A. Pichugov, “Sequences of operators bounded in measure”, Russian Acad. Sci. Sb. Math., 81:1 (1995), 35–58  crossref  isi
    13. V. B. Korotkov, “On the integral operators of the third kind”, Siberian Math. J., 44:5 (2003), 829–832  mathnet  crossref  mathscinet  zmath  isi
    14. S. Ya. Novikov, “$A$-Systems, Independent Functions, and Sets Bounded in Spaces of Measurable Functions”, Math. Notes, 75:1 (2004), 107–123  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. V. B. Korotkov, “One criterion for nuclearity of linear operators”, Siberian Math. J., 46:5 (2005), 857–862  mathnet  crossref  mathscinet  zmath  isi
    16. V. B. Korotkov, “On the functions of one selfadjoint integral operator”, Siberian Math. J., 49:5 (2008), 857–859  mathnet  crossref  mathscinet  isi  elib  elib
    17. S. V. Astashkin, K. E. Tikhomirov, “On Probability Analogs of Rosenthal's Inequality”, Math. Notes, 90:5 (2011), 644–650  mathnet  crossref  crossref  mathscinet  isi
    18. István Berkes, Michel Weber, “On series Σc k f(kx) and Khinchin’s conjecture”, Isr. J. Math, 2014  crossref
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