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Mat. Sb., 2006, Volume 197, Number 3, Pages 15–34 (Mi msb1537)  

This article is cited in 16 scientific papers (total in 16 papers)

The Hardy–Littlewood–Pólya inequality for analytic functions in Hardy–Sobolev spaces

K. Yu. Osipenko

Moscow State Aviation Technological University

Abstract: For a function of a complex variable analytic in a strip the extremum of the $L_2(\mathbb R)$ norm of the $k$th derivative is found under a constraint on the $L_2(\mathbb R)$-norm of the function and the norm of its $n$th derivative in the metric of the Hardy–Sobolev space. The closely connected problem of the optimal recovery of the $k$th derivative of a function in the Hardy–Sobolev class from the inaccurately given trace of this function on the real axis is also studied. An optimal recovery method is found.
Bibliography: 10 titles.

DOI: https://doi.org/10.4213/sm1537

Full text: PDF file (532 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2006, 197:3, 315–334

Bibliographic databases:

UDC: 517.5
MSC: 30H05, 41A46
Received: 29.03.2005 and 05.08.2005

Citation: K. Yu. Osipenko, “The Hardy–Littlewood–Pólya inequality for analytic functions in Hardy–Sobolev spaces”, Mat. Sb., 197:3 (2006), 15–34; Sb. Math., 197:3 (2006), 315–334

Citation in format AMSBIB
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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. E. V. Vvedenskaya, “Ob optimalnom vosstanovlenii resheniya uravneniya teploprovodnosti po netochno zadannoi temperature v razlichnye momenty vremeni”, Vladikavk. matem. zhurn., 8:1 (2006), 16–21  mathnet  mathscinet  elib
    2. N. D. Vysk, “O reshenii volnovogo uravneniya pri netochno zadannykh koeffitsientakh Fure funktsii, zadayuschei nachalnuyu formu struny”, Vladikavk. matem. zhurn., 8:4 (2006), 13–18  mathnet  mathscinet  elib
    3. Osipenko K.Yu., Wedenskaya E.V., “Optimal recovery of solutions of the generalized heat equation in the unit ball from inaccurate data”, J. Complexity, 23:4-6 (2007), 653–661  crossref  mathscinet  zmath  isi  elib  scopus
    4. N. D. Vysk, K. Yu. Osipenko, “Optimal Reconstruction of the Solution of the Wave Equation from Inaccurate Initial Data”, Math. Notes, 81:6 (2007), 723–733  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. E. A. Balova, “Optimal Reconstruction of the Solution of the Dirichlet Problem from Inaccurate Input Data”, Math. Notes, 82:3 (2007), 285–294  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal recovery of the solution of the heat equation from inaccurate data”, Sb. Math., 200:5 (2009), 665–682  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. Meftahi H., Wielonsky F., “Growth estimates in the Hardy-Sobolev space of an annular domain with applications”, J. Math. Anal. Appl., 358:1 (2009), 98–109  crossref  mathscinet  zmath  isi  elib  scopus
    8. E. V. Vvedenskaya, “On the optimal recovery of a solution of a system of linear homogeneous differential equations”, Differ. Equ., 45:2 (2009), 262–266  crossref  mathscinet  zmath  isi  elib  elib  scopus
    9. Osipenko K.Yu., Stessin M.I., “Hadamard and Schwarz type theorems and optimal recovery in spaces of analytic functions”, Constr. Approx., 31:1 (2010), 37–67  crossref  zmath  isi  scopus
    10. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “On the reconstruction of convolution-type operators from inaccurate information”, Proc. Steklov Inst. Math., 269 (2010), 174–185  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    11. I. Feki, H. Nfata, F. Wielonsky, “Optimal logarithmic estimates in the Hardy–Sobolev space of the disk and stability results”, Journal of Mathematical Analysis and Applications, 2012  crossref  mathscinet  isi  scopus
    12. Gonzalez-Vera P., Stessin M.I., “Joint Spectra of Toeplitz Operators and Optimal Recovery of Analytic Functions”, Constr. Approx., 36:1 (2012), 53–82  crossref  mathscinet  zmath  isi  elib  scopus
    13. K. Yu. Osipenko, “Optimal recovery of linear operators in non-Euclidean metrics”, Sb. Math., 205:10 (2014), 1442–1472  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    14. Akopyan R.R., “Optimal Recovery of a Derivative of An Analytic Function From Values of the Function Given With An Error on a Part of the Boundary”, Anal. Math., 44:1 (2018), 3–19  crossref  mathscinet  zmath  isi  scopus
    15. A. V. Arutyunov, K. Yu. Osipenko, “Recovering linear operators and Lagrange function minimality condition”, Siberian Math. J., 59:1 (2018), 11–21  mathnet  crossref  crossref  isi  elib
    16. R. R. Akopyan, “Optimalnoe vosstanovlenie analiticheskoi v poluploskosti funktsii po priblizhenno zadannym znacheniyam na chasti granichnoi pryamoi”, Tr. IMM UrO RAN, 24, no. 4, 2018, 19–33  mathnet  crossref  elib
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