Journal of Mathematical Sciences

, Volume 80, Issue 4, pp 1892–1896 | Cite as

Sarason's transform in a Sobolev space

  • I. A. Boricheva
  • E. M. Dyn'kin
Article

Abstract

The lassical Sarason transform is the canonical isomorphism of the model space H2/gqH2 (θ is an inner function generated by a single point mass) onto the standard L2 space. In the paper the image of the space of smooth functions H 2 1 ={f: f′ ε H2} under this transform is described in explicit terms. Pointwise estimates of the model operator in H 2 1 /θH 2 1 are obtained. Bibliography: 5 titles.

Keywords

Smooth Function Model Operator Single Point Sobolev Space Model Space 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    D. Sarason, “A remark on the Volterra operator,”J. Math. Anal. Appl.,12, 244–246 (1965).CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    N. K. Nikolski,Treatise on the Shift Operator, Berlin (1985).Google Scholar
  3. 3.
    V. P. Khavin, “On factorization of analytic functions smooth up to the boundary,”Zap. Nauchn. Semin. LOMI,23, 202–205 (1971).Google Scholar
  4. 4.
    I. A. Boricheva and E. M. Dyn'kin, “On a nonclassical free interpolation problem,”Algebra Analiz,4, No.5, 45–90 (1992).MathSciNetGoogle Scholar
  5. 5.
    E. M. Dyn'kin, “A constructive characterization of the classes of S. L. Sobolev and O. V. Besov,”Tr. MIAN,155, 41–76 (1981).MATHMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • I. A. Boricheva
  • E. M. Dyn'kin

There are no affiliations available

Personalised recommendations