Afrika Matematika

, Volume 30, Issue 1–2, pp 269–277 | Cite as

Operators and multipliers on weighted Bergman spaces

  • S. NaikEmail author
  • K. Rajbangshi


In 1992, Blasco considered a weighted Bergman space using Dini-weight function. He proved that a linear operator T on weighted Bergman space to any Banach space X is bounded if and only if certain one parameter fractional derivative of a single X-valued analytic function satisfy some growth condition. In this paper, we use a three parameters fractional derivative of a single X-valued analytic function and provide an equivalent condition. Our technique uses the Gaussian hypergeometric functions. Furthermore we supply some conditions on the parameters a, b and c under which the Gaussian hypergeometric functions F(abcz) are Dini-weight.


Hypergeometric functions Multipliers Bergman spaces 

Mathematics Subject Classification

33C05 42A45 30H20 47B38 


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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied SciencesGauhati UniversityGuwahatiIndia

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