Generalized Hilbert-Type Operator on Hardy Space

Authors

  • S. Naik Department of Applied Sciences, Gauhati University, Guwahati 781014, Assam
  • P. K. Nath Department of Applied Sciences, Gauhati University, Guwahati 781014, Assam

DOI:

https://doi.org/10.26713/cma.v6i1.271

Keywords:

Generalized Hilbert-type operator, Hardy Spaces

Abstract

If \(f\) be an analytic function on the unit disc \(\mathbb{D}\) with Taylor series expansion \(\displaystyle f(z) = \sum_{n=0}^\infty a_nz^n\), we consider the generalized Hilbert-type operator defined by \(\displaystyle\mathcal{H}_{a,b}(f)(z)=\sum_{n=0}^\infty\left(\sum_{k=0}^\infty \frac{\Gamma(n+a+1)\Gamma(n+k+1)}{\Gamma(n+1)\Gamma(n+k+b+2)}a_k\right)z^n\) where \(\Gamma\) denotes the Gamma function and \(a, b \in\mathbb{C}\). We find an upper bound for the norm of the generalized Hilbert-type operator on Hardy space.

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Published

08-08-2015
CITATION

How to Cite

Naik, S., & Nath, P. K. (2015). Generalized Hilbert-Type Operator on Hardy Space. Communications in Mathematics and Applications, 6(1), 1–8. https://doi.org/10.26713/cma.v6i1.271

Issue

Vol. 6 No. 1 (2015)

Section

Research Article

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