Rocky Mountain Journal of Mathematics

Compact Carleson measures from sparse sequences

Tesfa Mengestie

Full-text: Open access

Abstract

In [{\bf1}], Belov, Seip and the author studied the Carleson measures for certain spaces of analytic functions of which the de Branges spaces and the model subspaces of the Hardy space $H^2$ are prime examples. In this paper, we continue this line of research by studying the compact Carleson measures for such spaces.

Article information

Source
Rocky Mountain J. Math., Volume 44, Number 1 (2014), 223-234.

Dates
First available in Project Euclid: 2 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1401740500

Digital Object Identifier
doi:10.1216/RMJ-2014-44-1-223

Mathematical Reviews number (MathSciNet)
MR3216018

Zentralblatt MATH identifier
1297.30059

Subjects
Primary: 30E05: Moment problems, interpolation problems 46E22: Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]

Citation

Mengestie, Tesfa. Compact Carleson measures from sparse sequences. Rocky Mountain J. Math. 44 (2014), no. 1, 223--234. doi:10.1216/RMJ-2014-44-1-223. https://projecteuclid.org/euclid.rmjm/1401740500


Export citation

References

  • Y. Belov, T. Mengestie and K. Seip, Discrete Hilbert transforms on sparse sequences, Proc. Lond. Math. Soc., doi: 10.1112/plms/pdq053.
  • –––, Unitary discrete Hilbert transforms, J. Anal. Math. 112 (2010), 383-393.
  • A. Borichev and Yu. Lyubarskii, Riesz bases of reproducing kernels in Fock-type spaces, J. Inst. Math. Juss. 9 (2010), 449-461.
  • G. Chacon, E. Fricain and M. ShaBankhah, Carleson measures and reproducing kernels thesis in Dirichlet-type spaces, arXiv:1009.180v2, 2011.
  • T. Mengestie, Two weight discrete Hilbert transforms and systems of reproducing kernels, Ph.D. thesis, Norwegian University of Science and Technology, 2011.
  • E. Nordgren, Composition operators on Hilbert spaces, Lect. Notes Math. 693 (1978), Springer-Verlag, Berlin. \noindentstyle