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Advances in Pure and Applied Mathematics

Editor-in-Chief: Trimeche, Khalifa

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Integration operators from the space of Cauchy integral transforms to the Dirichlet space

Ajay K. Sharma / Anshu Sharma
Published Online: 2014-02-11 | DOI: https://doi.org/10.1515/apam-2013-0032


We consider the integration operator Ig,ϕ(n)f(z)=0zf(n)(ϕ(ζ))g(ζ)dζ, where g is a holomorphic function on the unit disk 𝔻, ϕ is a holomorphic self-map of 𝔻 and n{0}. The boundedness and compactness of Ig,ϕ(n) between the space of Cauchy integral transforms and the Dirichlet space are characterized.

Keywords: Integration operator; space of Cauchy integral transforms; Dirichlet space; boundedness; compactness.

MSC: 47B33; 46E10; 30D55

About the article

Received: 2013-10-09

Accepted: 2014-02-04

Published Online: 2014-02-11

Published in Print: 2014-03-01

Citation Information: Advances in Pure and Applied Mathematics, Volume 5, Issue 1, Pages 47–53, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam-2013-0032.

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