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Algebra i Analiz, 2009, Volume 21, Issue 6, Pages 47–65 (Mi aa1162)  
This article is cited in 9 scientific papers (total in 9 papers)

Research Papers

Radial growth of functions in the Korenblum space

A. Boricheva, Yu. Lyubarskiĭb, E. Malinnikovab, P. Thomasc

a Université Aix-Marseille, Marseille, France
b Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway
c Université Paul Sabatier, Touluose, France
Full-text PDF (295 kB) Citations (9)
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Abstract: The radial behavior of analytic and harmonic functions that admit a certain majorant in the unit disk is studied. We prove that the extremal growth or decay may occur only along small sets of radii and give precise estimates for these exceptional sets.
Keywords: spaces of analytic functions in the disk, harmonic functions, boundary values, Korenblum spaces.
Received: 27.03.2009
English version:
St. Petersburg Mathematical Journal, 2010, Volume 21, Issue 6, Pages 877–891
DOI: https://doi.org/10.1090/S1061-0022-2010-01123-3
Bibliographic databases:
Document Type: Article
MSC: 30J99, 31A20
Language: English
Citation: A. Borichev, Yu. Lyubarskiǐ, E. Malinnikova, P. Thomas, “Radial growth of functions in the Korenblum space”, Algebra i Analiz, 21:6 (2009), 47–65; St. Petersburg Math. J., 21:6 (2010), 877–891
Citation in format AMSBIB
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\paper Radial growth of functions in the Korenblum space
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\vol 21
\issue 6
\pages 47--65
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\pages 877--891
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Linking options:
  • https://www.mathnet.ru/eng/aa1162
  • https://www.mathnet.ru/eng/aa/v21/i6/p47
    • This publication is cited in the following 9 articles:
    1. Massimo A. Picardello, Maura Salvatori, Wolfgang Woess, “Polyharmonic potential theory on the Poincaré disk”, Journal of Functional Analysis, 286:9 (2024), 110362  crossref
    2. Hedenmalm H., Shimorin S., “Gaussian Analytic Functions and Operator Symbols of Dirichlet Type”, Adv. Math., 372 (2020), 107301  crossref  mathscinet  isi  scopus
    3. Mozolyako P., “Boundary Oscillations of Harmonic Functions in Lipschitz Domains”, Collect. Math., 68:3 (2017), 359–376  crossref  mathscinet  zmath  isi  scopus
    4. Twomey J.B., “Univalent Functions and Radial Growth”, Mathematika, 61:3 (2015), 531–546  crossref  mathscinet  zmath  isi  scopus
    5. Eikrem K.S., Malinnikova E., Mozolyako P.A., “Wavelet Characterization of Growth Spaces of Harmonic Functions”, J. Anal. Math., 122 (2014), 87–111  crossref  mathscinet  zmath  isi  elib  scopus
    6. Eikrem K.S., “Hadamard gap series in growth spaces”, Collect. Math., 64:1 (2013), 1–15  crossref  mathscinet  zmath  isi  elib  scopus
    7. Lyubarskii Yu., Malinnikova E., “Radial oscillation of harmonic functions in the Korenblum class”, Bull. London Math. Soc., 44:1 (2012), 68–84  crossref  zmath  isi  scopus
    8. Abakumov E., Doubtsov E., “Reverse estimates in growth spaces”, Math. Z., 271:1-2 (2012), 399–413  crossref  mathscinet  zmath  isi  elib  scopus
    9. Eikrem K.S., Malnnikova E., “Radial growth of harmonic functions in the unit ball”, Math. Scand., 110:2 (2012), 273–296  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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