Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

A note on interpolation by Bloch functions

Author(s): Daniel Pascuas
Journal: Proc. Amer. Math. Soc. 135 (2007), 2127-2130.
MSC (2000): Primary 30E05, 30D45; Secondary 30D50
Posted: March 2, 2007
MathSciNet review: 2299490
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We show that the positive part of a result on interpolation by Bloch functions due to B. Bøe and A. Nicolau is a direct consequence of C. Sundberg's description of the traces of BMOA functions on interpolating sequences for $H^\infty$ .

References:

1.: Bjarte Bøe and Artur Nicolau, Interpolation by functions in the Bloch space, J. Anal. Math. 94 (2004), 171-194. MR 2124459 (2005k:30052)
2.: Lennart Carleson, An interpolation problem for bounded analytic functions, Amer. J. Math. 80 (1958), 921-930. MR 0117349 (22:8129)
3.: Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York Inc., New York, 1969. MR 0257325 (41:1976)
4.: John B. Garnett and Peter W. Jones, BMO from dyadic BMO, Pacific J. Math. 99 (1982), no. 2, 351-371. MR 658065 (85d:42021)
5.: Eric P. Kronstadt, Interpolating sequences for functions satisfying a Lipschitz condition, Pacific J. Math. 63 (1976), no. 1, 169-177. MR 0412431 (54:557)
6.: N. G. Makarov, Probability methods in the theory of conformal mappings, Algebra i Analiz 1 (1989), no. 1, 3-59; translation in Leningrad Math. J. 1 (1990), no. 1, 1-56. MR 1015333 (90k:30008)
7.: Artur Nicolau, Radial behaviour of harmonic Bloch functions and their area function, Indiana Univ. Math. J. 48 (1999), no. 4, 1213-1236. MR 1757073 (2001f:42033)
8.: Kristian Seip, Interpolation and sampling in spaces of analytic functions, University Lecture Series, vol. 33, American Mathematical Society, Providence, RI, 2004. MR 2040080 (2005c:30038)
9.: Carl Sundberg, Values of BMOA functions on interpolating sequences, Michigan Math. J. 31 (1984), no. 1, 21-30. MR 736465 (85j:46035)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 30E05, 30D45, 30D50

Retrieve articles in all Journals with MSC (2000): 30E05, 30D45, 30D50

Additional Information:

Daniel Pascuas
Affiliation: Departament de Matemàtica Aplicada i Anàlisi, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain
Email: daniel_pascuas@ub.edu

DOI: 10.1090/S0002-9939-07-08722-9
PII: S 0002-9939(07)08722-9
Keywords: Interpolation, Bloch functions, BMOA
Received by editor(s): November 30, 2005
Received by editor(s) in revised form: March 16, 2006
Posted: March 2, 2007
Additional Notes: The author was partially supported by the DGI grant MTM2005-08984-C02-02 and the DURSI grant 2005SGR00611.
Communicated by: Juha M. Heinonen
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|