Advertisement

Journal of Mathematical Sciences

, Volume 243, Issue 6, pp 867–871 | Cite as

Extended Cesàro Operators Between Hardy and Bergman Spaces on the Complex Ball

  • E. S. DubtsovEmail author
Article
  • 6 Downloads

We characterize those holomorphic symbols g for which the extended Cesàro operator Vg maps the Hardy space Hp(B) into the weighted Bergman space\( {A}_{\beta}^q(B) \), 0 < p < q < ∞, β > −1, on the unit ball B of ℂd.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Aleman and J. A. Cima, “An integral operator on Hp and Hardy’s inequality,” J. Anal. Math., 85, 157–176 (2001).MathSciNetCrossRefGoogle Scholar
  2. 2.
    A. Aleman and A. G. Siskakis, “An integral operator on H p,” Complex Var. Theory Appl., 28, No. 2, 149–158 (1995).zbMATHGoogle Scholar
  3. 3.
    A. Aleman and A. G. Siskakis, “Integration operators on Bergman spaces,” Indiana Univ. Math. J., 46, No. 2, 337–356 (1997).MathSciNetCrossRefGoogle Scholar
  4. 4.
    Z. Hu, “Extended Cesàro operators on mixed norm spaces,” Proc. Amer. Math. Soc., 131, No. 7, 2171–2179 (2003).MathSciNetCrossRefGoogle Scholar
  5. 5.
    D. H. Luecking, “Embedding derivatives of Hardy spaces into Lebesgue spaces,” Proc. London Math. Soc. (3), 63, No. 3, 595–619 (1991).MathSciNetCrossRefGoogle Scholar
  6. 6.
    J. Pau, “Integration operators between Hardy spaces on the unit ball of ℂn,” J. Funct. Anal., 270, No. 1, 134–176 (2016).MathSciNetCrossRefGoogle Scholar
  7. 7.
    Ch. Pommerenke, “Schlichte Funktionen und analytische Funktionen von beschränkter mittlerer Oszillation,” Comment. Math. Helv., 52, No. 4, 591–602 (1977).MathSciNetCrossRefGoogle Scholar
  8. 8.
    Z. Wu, “Volterra operator, area integral and Carleson measures,” Sci. China Math., 54, No. 11, 2487–2500 (2011).MathSciNetCrossRefGoogle Scholar
  9. 9.
    J. Xiao, “Riemann–Stieltjes operators between weighted Bergman spaces,” in: Complex and Harmonic Analysis, DEStech Publ., Lancaster, Pennsylvania (2007), pp. 205–212.Google Scholar
  10. 10.
    K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Springer-Verlag, New York (2005).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.St. Petersburg Department of Steklov Institute of MathematicsSt. PeterburgRussia

Personalised recommendations