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VOLTERRA COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES

  • Li, Songxiao (Department of Mathematics Jia Ying University)
  • Published : 2008.01.31

Abstract

The boundedness and compactness of the Volterra composition operators between weighted Bergman spaces and Bloch type spaces are discussed in this paper.

Keywords

References

  1. A. Aleman and J. A. Cima, An integral operator on $H^p$ and Hardy's inequality, J. Anal. Math. 85 (2001), 157-176 https://doi.org/10.1007/BF02788078
  2. A. Aleman and A. G. Siskakis, An integral operator on $H^p$, Complex Variables Theory Appl. 28 (1995), no. 2, 149-158 https://doi.org/10.1080/17476939508814844
  3. A. Aleman and A. G. Siskakis, Integration operators on Bergman spaces, Indiana University Math. J. 46 (1997), no. 2, 337-356
  4. J. Arazy, S. D. Fisher, and J. Peetre, Mobius invariant function spaces, J. Reine Angew. Math. 363 (1985), 110-145
  5. C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, FL, 1995
  6. P. R. Halmos, Measure Theory, D. Van Nostrand Company, Inc., New York, N. Y., 1950
  7. Z. J. Hu, Extended Cesaro operators on mixed norm spaces, Proc. Amer. Math. Soc. 131 (2003), no. 7, 2171-2179 https://doi.org/10.1090/S0002-9939-02-06777-1
  8. Z. J. Hu, Extended Cesaro operators on the Bloch space in the unit ball of $C^n$, Acta Math. Scientia. Ser. B Engl. Ed. 23 (2003), no. 4, 561-566
  9. S. Li, Weighted composition operators from Bergman spaces into weighted Bloch spaces, Commun. Korean Math. Soc. 20 (2005), no. 1, 63-70 https://doi.org/10.4134/CKMS.2005.20.1.063
  10. K. Madigan and A. Matheson, Compact composition operators on the Bloch space, Trans. Amer. Math. Soc. 347 (1995), no. 7, 2679-2687 https://doi.org/10.2307/2154848
  11. S. Ohno, K. Stroethoff, and R. Zhao, Weighted composition operators between Bloch-type spaces, Rocky Mountain J. Math. 33 (2003), no. 1, 191-215 https://doi.org/10.1216/rmjm/1181069993
  12. F. Perez-Gonzalez and J. Rattya, Forelli-Rudin estimates, Carleson measures and F(p,q,s)-functions, J. Math. Anal. Appl. 315 (2006), no. 2, 394-414 https://doi.org/10.1016/j.jmaa.2005.10.034
  13. C. Pommerenke, Schlichte funktionen und analytische funktionen von beschrankter mittlerer oszillation, Comment. Math. Helv. 52 (1977), no. 4, 591-602 https://doi.org/10.1007/BF02567392
  14. J. H. Shapiro, Composition Operators and Classical Function Theory, Springer-Verlag, New York, 1993
  15. A. G. Siskakis and R. Zhao, A Volterra type operator on spaces of analytic functions, Function spaces(Edwardsville IL, 1998), 299-311, Contemp. Math. 232, Amer. Math. Soc. Providerce, RI, 1999
  16. S. Stevic, On an integral operator on the unit ball in $C^n$, J. Inequal. Appl. 2005 (2005), no. 1, 81-88 https://doi.org/10.1155/JIA.2005.81
  17. X. M. Tang and Z. J. Hu, Composition operators between Bergman spaces and q-Bloch spaces. (Chinese) Chinese Ann. Math. Ser. A 27 (2006), no. 1, 109-118
  18. J. Xiao, Riemann-Stieltjes operators on weighted Bloch and Bergman spaces of the unit ball, J. London. Math. Soc. (2) 70 (2004), no. 1, 199-214 https://doi.org/10.1112/S0024610704005484
  19. R. Yoneda, Pointwise multipliers from BMOA$^{\alpha}$ to BMOA$^{beta}$, Complex Var. Theory Appl. 49 (2004), no. 14, 1045-1061 https://doi.org/10.1080/02781070412331320448
  20. R. H. Zhao, Composition operators from Bloch type spaces to Hardy and Besov spaces, J. Math. Anal. Appl. 233 (1999), no. 2, 749-766 https://doi.org/10.1006/jmaa.1999.6341
  21. K. Zhu, Operator Theory in Function Spaces, Monographs and Textbooks in Pure and Applied Mathematics, 139. Marcel Dekker, Inc., New York, 1990
  22. K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Graduate Texts in Mathematics, 226. Springer-Verlag, New York, 2005

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