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Volterra-Type Operators on Zygmund Spaces


The boundedness and the compactness of the two integral operators;, where is an analytic function on the open unit disk in the complex plane, on the Zygmund space are studied.



  1. Duren PL: Theory of Hp Spaces, Pure and Applied Mathematics. Volume 38. Academic Press, New York, NY, USA; 1970:xii+258.

    Google Scholar 

  2. Pommerenke Ch: Schlichte Funktionen und analytische Funktionen von beschränkter mittlerer Oszillation. Commentarii Mathematici Helvetici 1977,52(4):591–602.

    Article  MathSciNet  MATH  Google Scholar 

  3. Aleman A, Siskakis AG: An integral operator on. Complex Variables. Theory and Application 1995,28(2):149–158. 10.1080/17476939508814844

    Article  MathSciNet  MATH  Google Scholar 

  4. Aleman A, Siskakis AG: Integration operators on Bergman spaces. Indiana University Mathematics Journal 1997,46(2):337–356.

    Article  MathSciNet  MATH  Google Scholar 

  5. Aleman A, Cima JA: An integral operator on and Hardy's inequality. Journal d'Analyse Mathématique 2001, 85: 157–176.

    Article  MathSciNet  MATH  Google Scholar 

  6. Benke G, Chang D-C: A note on weighted Bergman spaces and the Cesàro operator. Nagoya Mathematical Journal 2000, 159: 25–43.

    MathSciNet  MATH  Google Scholar 

  7. Chang D-C, Gilbert R, Tie J: Bergman projection and weighted holomorphic functions. In Reproducing Kernel Spaces and Applications, Oper. Theory Adv. Appl.. Volume 143. Birkhäuser, Basel, Switzerland; 2003:147–169.

    Chapter  Google Scholar 

  8. Chang D-C, Stević S: The generalized Cesàro operator on the unit polydisk. Taiwanese Journal of Mathematics 2003,7(2):293–308.

    MathSciNet  MATH  Google Scholar 

  9. Hu Z: Extended Cesàro operators on mixed norm spaces. Proceedings of the American Mathematical Society 2003,131(7):2171–2179. 10.1090/S0002-9939-02-06777-1

    Article  MathSciNet  MATH  Google Scholar 

  10. Hu Z: Extended Cesáro operators on the Bloch space in the unit ball of . Acta Mathematica Scientia. Series B. English Edition 2003,23(4):561–566.

    MathSciNet  MATH  Google Scholar 

  11. Li S: Riemann-Stieltjes operators from spaces to-Bloch spaces on the unit ball. Journal of Inequalities and Applications 2006, 2006: 14 pages.

    Article  Google Scholar 

  12. Li S, Stević S: Reimann-Stieltjies type integral operators on the unit ball in . Complex Variables Elliptic Functions 2007., 2:

    Google Scholar 

  13. Siskakis AG, Zhao R: A Volterra type operator on spaces of analytic functions. In Function Spaces (Edwardsville, IL, 1998), Contemp. Math.. Volume 232. American Mathematical Society, Providence, RI, USA; 1999:299–311.

    Google Scholar 

  14. Stević S: Cesàro averaging operators. Mathematische Nachrichten 2003,248/249(1):185–189. 10.1002/mana.200310013

    Article  Google Scholar 

  15. Stević S: On an integral operator on the unit ball in . Journal of Inequalities and Applications 2005,2005(1):81–88. 10.1155/JIA.2005.81

    MATH  Google Scholar 

  16. Stević S: Boundedness and compactness of an integral operator on a weighted space on the polydisc. Indian Journal of Pure and Applied Mathematics 2006,37(6):343–355.

    MathSciNet  MATH  Google Scholar 

  17. Tamrazov PM: Contour and solid structure properties of holomorphic functions of a complex variable. Russian Mathematical Surveys 1973,28(1):141–1731. 10.1070/RM1973v028n01ABEH001398

    Article  MathSciNet  MATH  Google Scholar 

  18. Cowen CC, MacCluer BD: Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics. CRC Press, Boca Raton, Fla, USA; 1995:xii+388.

    Google Scholar 

  19. Madigan K, Matheson A: Compact composition operators on the Bloch space. Transactions of the American Mathematical Society 1995,347(7):2679–2687. 10.2307/2154848

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Songxiao Li.

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Li, S., Stević, S. Volterra-Type Operators on Zygmund Spaces. J Inequal Appl 2007, 032124 (2007).

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