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Discrete Dynamics in Nature and Society
Volume 2008, Article ID 154263, 14 pages
http://dx.doi.org/10.1155/2008/154263
Research Article

On a New Integral-Type Operator from the Weighted Bergman Space to the Bloch-Type Space on the Unit Ball

Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 36/III, 11000 Beograd, Serbia

Received 1 May 2008; Accepted 20 July 2008

Academic Editor: Leonid Berezansky

Copyright © 2008 Stevo Stević. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. W. Rudin, Function Theory in the Unit Ball of n, vol. 241 of Grundlehren der Mathematischen Wissenschaften, Springer, New York, NY, USA, 1980. View at Zentralblatt MATH · View at MathSciNet
  2. A. L. Shields and D. L. Williams, “Bonded projections, duality, and multipliers in spaces of analytic functions,” Transactions of the American Mathematical Society, vol. 162, pp. 287–302, 1971. View at Publisher · View at Google Scholar · View at MathSciNet
  3. S. Stević, “Weighted composition operators between mixed norm spaces and Hα spaces in the unit ball,” Journal of Inequalities and Applications, vol. 2007, Article ID 28629, 9 pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  4. S. Stević, “Norm of weighted composition operators from Bloch space to Hμon the unit ball,” Ars Combinatoria, vol. 88, pp. 125–127, 2008. View at Google Scholar
  5. X. Tang, “Weighted composition operators between Bers-type spaces and Bergman spaces,” Applied Mathematics. A Journal of Chinese Universities, vol. 22, no. 1, pp. 61–68, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. S. Li, “Derivative-free characterizations of Bloch spaces,” Journal of Computational Analysis and Applications, vol. 10, no. 2, pp. 253–258, 2008. View at Google Scholar · View at MathSciNet
  7. S. Ohno, K. Stroethoff, and R. Zhao, “Weighted composition operators between Bloch-type spaces,” The Rocky Mountain Journal of Mathematics, vol. 33, no. 1, pp. 191–215, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. S. Stević, “On an integral operator on the unit ball in n,” Journal of Inequalities and Applications, vol. 2005, no. 1, pp. 81–88, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. Stević, “On Bloch-type functions with Hadamard gaps,” Abstract and Applied Analysis, vol. 2007, Article ID 39176, 8 pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  10. S. Yamashita, “Gap series and α-Bloch functions,” Yokohama Mathematical Journal, vol. 28, no. 1-2, pp. 31–36, 1980. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, vol. 226 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 2005. View at Zentralblatt MATH · View at MathSciNet
  12. C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, Fla, USA, 1995. View at Zentralblatt MATH · View at MathSciNet
  13. D. D. Clahane and S. Stević, “Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball,” Journal of Inequalities and Applications, vol. 2006, Article ID 61018, 11 pages, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. S. Li and S. Stević, “Composition followed by differentiation between Bloch type spaces,” Journal of Computational Analysis and Applications, vol. 9, no. 2, pp. 195–205, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. S. Li and S. Stević, “Weighted composition operators from Bergman-type spaces into Bloch spaces,” Proceedings of the Indian Academy of Sciences. Mathematical Sciences, vol. 117, no. 3, pp. 371–385, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. S. Li and S. Stević, “Weighted composition operators from α-Bloch space to H on the polydisc,” Numerical Functional Analysis and Optimization, vol. 28, no. 7-8, pp. 911–925, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. S. Li and S. Stević, “Weighted composition operators from H to the Bloch space on the polydisc,” Abstract and Applied Analysis, vol. 2007, Article ID 48478, 13 pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  18. S. Li and S. Stević, “Generalized composition operators on Zygmund spaces and Bloch type spaces,” Journal of Mathematical Analysis and Applications, vol. 338, no. 2, pp. 1282–1295, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. S. Li and S. Stević, “Weighted composition operators between H and α-Bloch spaces in the unit ball,” to appear in Taiwanese Journal of Mathematics.
  20. S. Stević, “Composition operators between H and a-Bloch spaces on the polydisc,” Zeitschrift für Analysis und ihre Anwendungen, vol. 25, no. 4, pp. 457–466, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. S.-I. Ueki and L. Luo, “Compact weighted composition operators and multiplication operators between Hardy spaces,” Abstract and Applied Analysis, vol. 2008, Article ID 196498, 12 pages, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  22. X. Zhu, “Generalized weighted composition operators from Bloch type spaces to weighted Bergman spaces,” Indian Journal of Mathematics, vol. 49, no. 2, pp. 139–150, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. X. Zhu, “Products of differentiation, composition and multiplication from Bergman type spaces to Bers type spaces,” Integral Transforms and Special Functions, vol. 18, no. 3, pp. 223–231, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. Ch. Pommerenke, “Schlichte Funktionen und analytische Funktionen von beschränkter mittlerer Oszillation,” Commentarii Mathematici Helvetici, vol. 52, no. 1, pp. 591–602, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. A. Aleman and J. A. Cima, “An integral operator on Hp and Hardy's inequality,” Journal d'Analyse Mathématique, vol. 85, pp. 157–176, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. A. G. Siskakis and R. Zhao, “A Volterra type operator on spaces of analytic functions,” in Function Spaces (Edwardsville, IL, 1998), vol. 232 of Contemporary Mathematics, pp. 299–311, American Mathematical Society, Providence, RI, USA, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. D.-C. Chang, S. Li, and S. Stević, “On some integral operators on the unit polydisk and the unit ball,” Taiwanese Journal of Mathematics, vol. 11, no. 5, pp. 1251–1285, 2007. View at Google Scholar · View at MathSciNet
  28. D.-C. Chang and S. Stević, “Estimates of an integral operator on function spaces,” Taiwanese Journal of Mathematics, vol. 7, no. 3, pp. 423–432, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. D.-C. Chang and S. Stević, “The generalized Cesàro operator on the unit polydisk,” Taiwanese Journal of Mathematics, vol. 7, no. 2, pp. 293–308, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. D.-C. Chang and S. Stević, “Addendum to the paper: “A note on weighted Bergman spaces and the Cesàro operator”,” Nagoya Mathematical Journal, vol. 180, pp. 77–90, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. Z. Hu, “Extended Cesàro operators on mixed norm spaces,” Proceedings of the American Mathematical Society, vol. 131, no. 7, pp. 2171–2179, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. Z. Hu, “Extended Cesàro operators on the Bloch space in the unit ball of n,” Acta Mathematica Scientia. Series B, vol. 23, no. 4, pp. 561–566, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. S. Li and S. Stević, “Riemann-Stieltjes operators on Hardy spaces in the unit ball of n,” Bulletin of the Belgian Mathematical Society. Simon Stevin, vol. 14, no. 4, pp. 621–628, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  34. S. Li and S. Stević, “Riemann-Stieltjes-type integral operators on the unit ball in n,” Complex Variables and Elliptic Equations, vol. 52, no. 6, pp. 495–517, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  35. S. Stević, “Boundedness and compactness of an integral operator on a weighted space on the polydisc,” Indian Journal of Pure and Applied Mathematics, vol. 37, no. 6, pp. 343–355, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  36. S. Stević, “Boundedness and compactness of an integral operator in a mixed norm space on the polydisk,” Sibirskiĭ Matematicheskiĭ Zhurnal, vol. 48, no. 3, pp. 694–706, 2007. View at Google Scholar · View at MathSciNet
  37. X. Tang, “Extended Cesàro operators between Bloch-type spaces in the unit ball of n,” Journal of Mathematical Analysis and Applications, vol. 326, no. 2, pp. 1199–1211, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  38. Z. Hu, “Extended Cesàro operators on Bergman spaces,” Journal of Mathematical Analysis and Applications, vol. 296, no. 2, pp. 435–454, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  39. S. Li and S. Stević, “Integral type operators from mixed-norm spaces to α-Bloch spaces,” Integral Transforms and Special Functions, vol. 18, no. 7, pp. 485–493, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  40. S. Li and S. Stević, “Compactness of Riemann-Stieltjes operators between F(p,q,s) spaces and α-Bloch spaces,” Publicationes Mathematicae Debrecen, vol. 72, no. 1-2, pp. 111–128, 2008. View at Google Scholar · View at MathSciNet
  41. S. Li and S. Stević, “Riemann-Stieltjes operators between mixed norm spaces,” Indian Journal of Mathematics, vol. 50, no. 1, pp. 177–188, 2008. View at Google Scholar · View at MathSciNet
  42. S. Stević, “Products of integral type operators and composition operators from the mixed norm space to Bloch-type spaces,” to appear.
  43. F. Beatrous and J. Burbea, “Holomorphic Sobolev spaces on the ball,” Dissertationes Mathematicae, vol. 276, pp. 1–60, 1989. View at Google Scholar · View at MathSciNet
  44. J.-H. Shi, “Inequalities for the integral means of holomorphic functions and their derivatives in the unit ball of n,” Transactions of the American Mathematical Society, vol. 328, no. 2, pp. 619–637, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  45. K. L. Avetisyan, “Continuous inclusions and Bergman type operators in n-harmonic mixed norm spaces on the polydisc,” Journal of Mathematical Analysis and Applications, vol. 291, no. 2, pp. 727–740, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  46. K. Avetisyan and S. Stević, “Holomorphic functions on the mixed norm spaces on the polydisc—II,” to appear in Journal of Computational Analysis and Applications.
  47. Z. Hu, “Estimates for the integral mean of harmonic functions on bounded domains in n,” Science in China. Series A, vol. 38, no. 1, pp. 36–46, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  48. S. Stević, “Weighted integrals of holomorphic functions on the polydisc,” Zeitschrift für Analysis und ihre Anwendungen, vol. 23, no. 3, pp. 577–587, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  49. S. Stević, “Weighted integrals of holomorphic functions on the polydisc—II,” Zeitschrift für Analysis und ihre Anwendungen, vol. 23, no. 4, pp. 775–782, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  50. G. Ren and U. Kähler, “Hardy-Littlewood inequalities and Qp-spaces,” Zeitschrift für Analysis und ihre Anwendungen, vol. 24, no. 2, pp. 375–388, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  51. S. Stević, “Comment on: “Hardy-Littlewood inequalities and Qp-spaces”,” Zeitschrift für Analysis und ihre Anwendungen, vol. 26, no. 4, pp. 473–480, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  52. S. Stević, “Holomorphic functions on the mixed norm spaces on the polydisc,” Journal of the Korean Mathematical Society, vol. 45, no. 1, pp. 63–78, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  53. K. Madigan and A. Matheson, “Compact composition operators on the Bloch space,” Transactions of the American Mathematical Society, vol. 347, no. 7, pp. 2679–2687, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet