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Russian Mathematical Surveys, 1970, Volume 25, Issue 6, Pages 125–187
DOI: https://doi.org/10.1070/RM1970v025n06ABEH001270
(Mi rm5429)
 

This article is cited in 33 scientific papers (total in 34 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.
Received: 16.02.1970
Bibliographic databases:
Document Type: Article
UDC: 517.43
Language: English
Original paper language: Russian
Citation: E. M. Nikishin, “Resonance theorems and superlinear operators”, 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 Russian Math. Surveys
\yr 1970
\vol 25
\issue 6
\pages 125--187
\mathnet{http://mi.mathnet.ru/eng/rm5429}
\crossref{https://doi.org/10.1070/RM1970v025n06ABEH001270}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=296584}
\zmath{https://zbmath.org/?q=an:0222.47024|0226.47042}
Linking options:
  • https://www.mathnet.ru/eng/rm5429
  • https://doi.org/10.1070/RM1970v025n06ABEH001270
  • https://www.mathnet.ru/eng/rm/v25/i6/p129
  • This publication is cited in the following 34 articles:
    1. Stefan Buschenhenke, “Factorization in Fourier restriction theory and near extremizers”, Mathematische Nachrichten, 297:1 (2024), 195  crossref
    2. Fausto Di Biase, Steven G. Krantz, “Foundations of Fatou Theory and a Tribute to the Work of E. M. Stein on Boundary Behavior of Holomorphic Functions”, J Geom Anal, 31:7 (2021), 7184  crossref
    3. Hiroshi Ando, Yasumichi Matsuzawa, Andreas Thom, Asger Törnquist, “Unitarizability, Maurey–Nikishin factorization, and Polish groups of finite type”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2020:758 (2020), 223  crossref
    4. István Berkes, Number Theory – Diophantine Problems, Uniform Distribution and Applications, 2017, 137  crossref
    5. Alexander Shamov, “On Gaussian multiplicative chaos”, Journal of Functional Analysis, 270:9 (2016), 3224  crossref
    6. István Berkes, Michel Weber, “On series Σc k f(kx) and Khinchin’s conjecture”, Isr. J. Math, 2014  crossref
    7. 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
    8. 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
    9. V. B. Korotkov, “One criterion for nuclearity of linear operators”, Siberian Math. J., 46:5 (2005), 857–862  mathnet  crossref  mathscinet  zmath  isi
    10. 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
    11. Lahcène Mezrag, “Factorization of operator valued Lp for 0 ≤ p < 1”, Mathematische Nachrichten, 266:1 (2004), 60  crossref
    12. V. B. Korotkov, “On the integral operators of the third kind”, Siberian Math. J., 44:5 (2003), 829–832  mathnet  crossref  mathscinet  zmath  isi
    13. Teresa Martínez, “On weighted inequalities for martingale transform operators”, Mathematische Nachrichten, 251:1 (2003), 52  crossref
    14. N. Kalton, I. Verbitsky, “Nonlinear equations and weighted norm inequalities”, Trans. Amer. Math. Soc., 351:9 (1999), 3441  crossref
    15. Alexander Koldobsky, “A Banach subspace of 𝐿_{1/2} which does not embed in 𝐿₁ (isometric version)”, Proc. Amer. Math. Soc., 124:1 (1996), 155  crossref
    16. Alexander Olevskiǐ, Geometric Aspects of Functional Analysis, 1995, 199  crossref
    17. S. A. Pichugov, “Sequences of operators bounded in measure”, Russian Acad. Sci. Sb. Math., 81:1 (1995), 35–58  mathnet  crossref  mathscinet  zmath  isi
    18. J. LINDENSTRAUSS, V.D. MILMAN, Handbook of Convex Geometry, 1993, 1149  crossref
    19. 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
    20. 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
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