Connections of Linear Operators Defined by Analytic Functions with \(Q_p\) Spaces

Volume 10, Issue 1, pp 78-84 http://dx.doi.org/10.22436/jmcs.010.01.08

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2580 Downloads
• 4533 Views

Authors

Z. Orouji - Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran. R. Aghalary - Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran. A. Ebadian - Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran.

Abstract

This paper is concerned mainly with the linear operators \(I_f^{\gamma , \alpha}\) and \(J_f^{\gamma , \alpha}\) of analytic function \(f\).The norm of \(I_f^{\gamma , \alpha}\) and \(J_f^{\gamma , \alpha}\) on some analytic function spaces is computed in this paper. We study the relation between \(I_f^{\gamma , \alpha}\) and \(J_f^{\gamma , \alpha}\) operators, the \(\beta(\lambda)\) spaces and \(Q_p\) spaces \((0<p<\infty)\).

Share and Cite

Keywords

• Integral operator
• \(Q_p\) spaces
• Pre-Schwarzian derivative.

MSC

•  30H05
•  30H25
•  32A37
•  47B38

References

• [1] R. Aulaskari, P. Lappan, Criteria for an analytic function to be Bloch and a harmonic or meromorphic function to be normal, Complex Analysis and Its Applications, 305 (1994), 136-146.
  • MathSciNet
  • Google Scholar


• [2] R. Aulaskari, P. Lappan, J. Xiao, R. Zhao, On 𝛼-Bloch spaces and multipliers of Dirichlet spaces, J. Math.Anal.Appl. , 209(1) (1997), 103-121.
  • View Article
  • MathSciNet
  • Google Scholar


• [3] J. Becker, Lownersche Differentialgleichung und quasikonform fortsetzbare schlichte funktionen, J. reine Angew. Math., 255 (1972), 23-43.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] P. L. Duren, Theory of \(H^p\) Spaces, Academic Press, New York, London(1970), Reprint:Dover, Mineola, New York (2000)
  • Google Scholar


• [5] B. J. Garnett, Bounded Analytic Functions, Graduate Texts in Mathematics, Springer, Revised first edition. , Berlin (2007)
  • Google Scholar


• [6] D. Girela, Analytic functions of bounded mean oscillation, In: Aulaskari, R. (ed.) Complex Function Spaces, Mekrijarvi 1997. Univ. Joensuu Dept. Math. Rep. Ser., 4 (2001), 61-170.
  • Google Scholar


• [7] C. Hammond , The norm of a composition operator with linear symbol acting on the Dirichlet space, J. Math. Anal. Appl. , 303 (2005), 499-508.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] Y. C. Kim, T. Sugawa, Growth and coefficient estimates for uniformly locally univalent functions on the unit disk, Rocky Mountain J. Math., 32 (2002), 179-200.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] Y. C. Kim, T. Sugawa , Uniformly locally univalent functions and Hardy spaces, J. Math. Anal. Appl. , 353 (2009), 61-67.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] F. John, L. Nirenberg, On functions of bounded mean oscillation, Commun. Pure Appl. Math., 14 (1961), 415-426.
  • View Article
  • Google Scholar


• [11] H. Li, S. Li , Norm of an integral operators on some analytic function spaces on the unit disk , Journal of Inequalities and Applications, 342 (2013), 1-7.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [12] S. Li, S. Stevic, Integral type operators from mixed-norm spaces to 𝛼-Bloch spaces, Integral Transforms Spec. Funct. , 18(7) (2007), 485-493.
  • View Article
  • Google Scholar


• [13] Ch. Pommerenke, Schlichtefunktionen und analytische funktionen von Bechranktermittlereroszillation, Comment. Math. Helv., 52 (1977), 591-602.
  • View Article
  • Google Scholar


• [14] D. Sarason, Function theory on the unit circle, Virginia Polytechnic Institute and State University. Blacksburg, Virginia (1978)
  • Google Scholar


• [15] S. Stevic, On an integral operator between Bloch-type spaces on the unit ball, Bull. Sci. Math. , 134 (2010), 329-339.
  • View Article
  • Google Scholar


• [16] J. Xiao, Holomorphic Q Classes, Lecture Notes in Mathematics, vol. 1767. Springer, Berlin (2001)
  • View Article
  • MathSciNet
  • Google Scholar


• [17] J. Xiao, Ceometric Q Functions, Frontiers in Mathematics, Birkhauser, Basel (2006)
  • MathSciNet
  • Google Scholar


• [18] K. Zhu, Operator theory in function spaces, Marcel Dekker, New York (1990). Reprint: Math. Surveys and Monographs, vol. 138. American Mathematical Society, Providence (2007)
  • View Article
  • MathSciNet
  • Google Scholar


• [19] K. Zhu, Bloch type spaces of analytic functions, Rocky Mt. J. Math., 23 (1993), 1143-1177.
  • View Article
  • MathSciNet
  • Google Scholar