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Radial growth of functions in the Korenblum space


Authors: A. Borichev, Yu. Lyubarskii, E. Malinnikova and P. Thomas
Original publication: Algebra i Analiz, tom 21 (2009), nomer 6.
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
Published electronically: September 22, 2010
MathSciNet review: 2604542
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Abstract | References | Similar Articles | Additional Information

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.


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Additional 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
Email: eugenia@math.ntnu.no

P. Thomas
Affiliation: Université Paul Sabatier, 31062, Touluose Cedex 9, France
Email: pthomas@math.univ-toulouse.fr

DOI: https://doi.org/10.1090/S1061-0022-2010-01123-3
Keywords: Spaces of analytic functions in the disk, harmonic functions, boundary values, Korenblum spaces
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.
Dedicated: Dedicated to Victor Petrovich Havin on the occasion of his 75th birthday
Article copyright: © Copyright 2010 American Mathematical Society

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