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Advances in Pure and Applied Mathematics

Editor-in-Chief: Trimeche, Khalifa

Editorial Board: Aldroubi, Akram / Anker, Jean-Philippe / Aouadi, Saloua / Bahouri, Hajer / Baklouti, Ali / Bakry, Dominique / Baraket, Sami / Ben Abdelghani, Leila / Begehr, Heinrich / Beznea, Lucian / Bezzarga, Mounir / Bonami, Aline / Demailly, Jean-Pierre / Fleckinger, Jacqueline / Gallardo, Leonard / Ismail, Mourad / Jarboui, Noomen / Jouini, Elyes / Karoui, Abderrazek / Kamoun, Lotfi / Kobayashi, Toshiyuki / Maday, Yvon / Marzougui, Habib / Mili, Maher / Mustapha, Sami / Ovsienko, Valentin / Peigné, Marc / Pouzet, Maurice / Radulescu, Vicentiu / Schwartz, Lionel / Sifi, Mohamed / Zaag, Hatem / Zarati, Said

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1869-6090
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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

Abstract.

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, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam-2013-0032.

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© 2014 by Walter de Gruyter Berlin/Boston. Copyright Clearance Center

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