An interpolation theorem for Hilbert spaces with Nevanlinna-Pick kernel
HTML articles powered by AMS MathViewer
- by Bjarte Bøe PDF
- Proc. Amer. Math. Soc. 133 (2005), 2077-2081 Request permission
Abstract:
We prove an interpolation theorem for Hilbert spaces of analytic functions that have the Nevanlinna-Pick property. This result applies to Dirichlet and Dirichlet-type spaces, and in particular a short proof of the theorem by Marshall-Sundberg on interpolating sequences is obtained.References
- Jim Agler and John E. McCarthy, Complete Nevanlinna-Pick kernels, J. Funct. Anal. 175 (2000), no. 1, 111–124. MR 1774853, DOI 10.1006/jfan.2000.3599
- Jim Agler and John E. McCarthy, Pick interpolation and Hilbert function spaces, Graduate Studies in Mathematics, vol. 44, American Mathematical Society, Providence, RI, 2002. MR 1882259, DOI 10.1090/gsm/044
- C. Bishop, Interpolating sequences for the Dirichlet space and its multipliers, Preprint, 1994.
- Bjarte Böe, Interpolating sequences for Besov spaces, J. Funct. Anal. 192 (2002), no. 2, 319–341. MR 1923404, DOI 10.1006/jfan.2002.3905
- William S. Cohn, Interpolation and multipliers on Besov and Sobolev spaces, Complex Variables Theory Appl. 22 (1993), no. 1-2, 35–45. MR 1277009, DOI 10.1080/17476939308814644
- C. Sundberg and D. Marshall, Interpolating sequences for the multipliers of the Dirichlet space, see www.math.washington.edu/$\sim$marshall/preprints/preprints.html.
- N. K. Nikol′skiĭ, Treatise on the shift operator, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 273, Springer-Verlag, Berlin, 1986. Spectral function theory; With an appendix by S. V. Hruščev [S. V. Khrushchëv] and V. V. Peller; Translated from the Russian by Jaak Peetre. MR 827223, DOI 10.1007/978-3-642-70151-1
- Nicola Arcozzi, Richard Rochberg, and Eric Sawyer, Carleson measures for analytic Besov spaces, Rev. Mat. Iberoamericana 18 (2002), no. 2, 443–510. MR 1949836, DOI 10.4171/RMI/326
- H. S. Shapiro and A. L. Shields, On the zeros of functions with finite Dirichlet integral and some related function spaces, Math. Z. 80 (1962), 217–229. MR 145082, DOI 10.1007/BF01162379
- Jie Xiao, The $\overline \partial$-problem for multipliers of the Sobolev space, Manuscripta Math. 97 (1998), no. 2, 217–232. MR 1651405, DOI 10.1007/s002290050098
Additional Information
- Bjarte Bøe
- Affiliation: Department of Mathematics, University of California Los Angeles, Box 951555, Los Angeles, California 90095-1555
- Email: bjarteb@math.ucla.edu
- Received by editor(s): September 30, 2003
- Received by editor(s) in revised form: March 12, 2004
- Published electronically: January 31, 2005
- Communicated by: Juha M. Heinonen
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 2077-2081
- MSC (2000): Primary 30H05, 46E22
- DOI: https://doi.org/10.1090/S0002-9939-05-07722-1
- MathSciNet review: 2137874