Radial growth of functions in the Korenblum space
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- by A. Borichev, Yu. Lyubarskii, E. Malinnikova and P. Thomas
- St. Petersburg Math. J. 21 (2010), 877-891
- DOI: https://doi.org/10.1090/S1061-0022-2010-01123-3
- Published electronically: September 22, 2010
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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.References
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Bibliographic Information
- A. Borichev
- Affiliation: Université Aix-Marseille, 39 Rue Joliot Curie, 13453, Marseille Cedex 13, France
- Email: borichev@cmi.univ-mrs.fr
- Yu. Lyubarskii
- Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491, Trondheim, Norway
- Email: yura@math.ntnu.no
- E. Malinnikova
- Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491, Trondheim, Norway
- MR Author ID: 630914
- ORCID: 0000-0002-6126-1592
- Email: eugenia@math.ntnu.no
- P. Thomas
- Affiliation: Université Paul Sabatier, 31062, Touluose Cedex 9, France
- MR Author ID: 238303
- Email: pthomas@math.univ-toulouse.fr
- Received by editor(s): March 27, 2009
- Published electronically: September 22, 2010
- Additional Notes: A. B. was partially supported by the ANR project DYNOP
Yu. L. was partly supported by the Research Council of Norway, grants 160192/V30 and 177355/V30.
E. M. was partly supported by the Research Council of Norway, grants 160192/V30 and 177355/V30. - © Copyright 2010 American Mathematical Society
- Journal: St. Petersburg Math. J. 21 (2010), 877-891
- MSC (2010): Primary 30J99, 31A20
- DOI: https://doi.org/10.1090/S1061-0022-2010-01123-3
- MathSciNet review: 2604542
Dedicated: Dedicated to Victor Petrovich Havin on the occasion of his 75th birthday