DOI QR코드

DOI QR Code

GENERALIZED WEIGHTED COMPOSITION OPERATORS FROM AREA NEVANLINNA SPACES TO WEIGHTED-TYPE SPACES

  • Weifeng, Yang (Department of Mathematics and Physics Hunan Institute of Engineering) ;
  • Weiren, Yan (Department of Mathematics and Physics Hunan Institute of Engineering)
  • 투고 : 2010.06.30
  • 발행 : 2011.11.30

초록

Let $H(\mathbb{D})$ denote the class of all analytic functions on the open unit disk $\mathbb{D}$ of the complex plane $\mathbb{C}$. Let n be a nonnegative integer, ${\varphi}$ be an analytic self-map of $\mathbb{D}$ and $u{\in}H(\mathbb{D})$. The generalized weighted composition operator is defined by $$D_{{\varphi},u}^nf=uf^{(n)}{\circ}{\varphi},\;f{\in}H(\mathbb{D})$$. The boundedness and compactness of the generalized weighted composition operator from area Nevanlinna spaces to weighted-type spaces and little weighted-type spaces are characterized in this paper.

참고문헌

  1. K. D. Bierstedt, J. Bonet, and J. Taskinen, Associated weights and spaces of holomorphic functions, Studia Math. 127 (1998), no. 2, 137-168.
  2. B. Choe, H. Koo, and W. Smith, Carleson measure for the area Nevalinna spaces and applications, J. Anal. Math. 104 (2008), 207-233. https://doi.org/10.1007/s11854-008-0022-8
  3. D. Clahane and S. Stevic, Norm equivalence and composition operators between Bloch/Lipschitz spaces of the unit ball, J. Inequal. Appl. 2006 (2006), Article ID 61018.
  4. C. Cowen and B. MacCluer, Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, 1995.
  5. X. Fu and X. Zhu, Weighted composition operators on some weighted spaces in the unit ball, Abstr. Appl. Anal. 2008 (2008), Article ID 605807.
  6. R. A. Hibschweiler and N. Portnoy, Composition followed by differentiation between Bergman and Hardy spaces, Rochy Mountain J. Math. 35 (2005), no. 3, 843-855. https://doi.org/10.1216/rmjm/1181069709
  7. H. Jarchow and J. Xiao, Composition operators between Nevanlinna classes and Bergman spaces with weights, J. Operator Theory 46 (2001), no. 3, suppl., 605-618.
  8. S. Li and S. Stevic, Composition followed by differentiation between Bloch type space, J. Comput. Anal. Appl. 9 (2007), no. 2, 195-205.
  9. S. Li and S. Stevic, Weighted composition operators from $\alpha$-Bloch space to $H^\infty$ on the polydisk, Numer. Funct. Anal. Optim. 28 (2007), no. 7-8, 911-925. https://doi.org/10.1080/01630560701493222
  10. S. Li and S. Stevic, Weighted composition operators from Bergman-type spaces into Bloch spaces, Proc. Indian Acad. Sci. Math. Sci. 117 (2007), no. 3, 371-385. https://doi.org/10.1007/s12044-007-0032-y
  11. S. Li and S. Stevic, Weighted composition operators from $H^\infty$ to the Bloch space on the polydisc, Abstr. Appl. Anal. 2007 (2007), Article ID 48478.
  12. S. Li and S. Stevic, Weighted composition operators between $H^\infty$ and $\alpha$-Bloch spaces in the unit ball, Taiwanese J. Math. 12 (2008), no. 7, 1625-1639. https://doi.org/10.11650/twjm/1500405075
  13. S. Li and S. Stevic, Weighted composition operators from Zygmund spaces into Bloch spaces, Appl. Math. Comput. 206 (2008), no. 2, 825-831. https://doi.org/10.1016/j.amc.2008.10.006
  14. S. Li and S. Stevic, Composition followed by differentiation from mixed-norm spaces to $\alpha$-Bloch spaces, Matematicheskii Sbornik 199 (2008), no. 12, 117-128. https://doi.org/10.4213/sm3794
  15. Y. Liu and Y. Yu, Composition followed by differentiation between $H^\infty$ and Zygmund spaces, Complex Anal. Oper. Theory, (2010).
  16. Z. Lou, Composition operators on Bloch type spaces, Analysis (Munich) 23 (2003), no. 1, 81-95.
  17. 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
  18. S. Ohno, Weighted composition operators between $H^\infty$ and the Bloch space, Taiwanese J. Math. 5 (2001), no. 3, 555-563. https://doi.org/10.11650/twjm/1500574949
  19. S. Ohno, Products of composition and differentiation between Hardy spaces, Bull. Austral. Math. Soc. 73 (2006), no. 2, 235-243. https://doi.org/10.1017/S0004972700038818
  20. 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
  21. A. L. Shields and D. L. Williams, Bounded projections, duality, and multipliers in spaces of analytic functions, J. Reine Angew. Math. 299/300 (1978), 256-279.
  22. S. Stevic, Weighted composition operators between mixed norm spaces and $H^{\infty}_\alpha$ spaces in the unit ball, J. Inequal. Appl. 2007 (2007), Article ID 28629. https://doi.org/10.1155/2007/28629
  23. S. Stevic, Weighted composition operators from weighted Bergman spaces to weighted-type spaces on the unit ball, Appl. Math. Comput. 212 (2009), no. 2, 499-504. https://doi.org/10.1016/j.amc.2009.02.057
  24. S. Stevic, Norm and essential norm of composition followed by differentiation from $\alpha$-Bloch spaces to $H^{\infty}_\mu$, Appl. Math. Comput. 207 (2009), no. 1, 225-229. https://doi.org/10.1016/j.amc.2008.10.032
  25. S. Stevic, Weighted differentiation composition operators from mixed-norm spaces to weighted-type spaces, Appl. Math. Comput. 211 (2009), no. 1, 222-233. https://doi.org/10.1016/j.amc.2009.01.061
  26. S. Stevic, Norm of weighted composition operators from $\alpha$-Bloch spaces to weighted-type spaces, Appl. Math. Comput. 215 (2009), no. 2, 818-820. https://doi.org/10.1016/j.amc.2009.06.005
  27. S. Stevic, Products of composition and differentiation operators on the weighted Bergman space, Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 4, 623-635.
  28. S. Stevic, Composition followed by differentiation from $H^{\infty}$ and the Bloch space to nth weighted-type spaces on the unit disk, Appl. Math. Comput. 216 (2010), no. 12, 3450-3458. https://doi.org/10.1016/j.amc.2010.03.117
  29. S. Stevic, Weighted differentiation composition operators from $H^{\infty}$ and Bloch spaces to nth weighted-type spaces on the unit disk, Appl. Math. Comput. 216 (2010), no. 12, 3634-3641. https://doi.org/10.1016/j.amc.2010.05.014
  30. S. Stevic, Weighted differentiation composition operators from the mixed-norm space to the nth weigthed-type space on the unit disk, Abstr. Appl. Anal. 2010 (2010), Article ID 246287.
  31. S. Stevic, Weighted composition operators from the Bergman-Privalov-Type spaces to weighted-type spaces on the unit ball, Appl. Math. Comput. in press.
  32. J. Xiao, Compact composition operators on the area-Nevanlinna class, Exposition. Math. 17 (1999), no. 3, 255-264.
  33. J. Xiao, Composition operators: $N_\alpha$ to the Bloch space to $Q_\beta$, Studia Math. 139 (2000), no. 3, 245-260. https://doi.org/10.4064/sm-139-3-245-260
  34. W. Yang, Weighted composition operators from Bloch-type spaces to weighted-type spaces, Ars Combin. 92 (2009), 415-423.
  35. W. Yang, Products of composition and differentiation operators from $Q_K$(p, q) spaces to Bloch-type spaces, Abstr. Appl. Anal. 2009 (2009), Art. ID 741920, 14 pp.
  36. K. Zhu, Operator Theory in Function Spaces, Marcel Dekker, Inc. Pure and Applied Mathematics 139, New York and Basel, 1990.
  37. X. Zhu, Weighted composition operators between $H^{\infty}$ and Bergman type spaces, Commun. Korean Math. Soc. 21 (2006), no. 4, 719-727. https://doi.org/10.4134/CKMS.2006.21.4.719
  38. X. Zhu, Products of differentiation, composition and multiplication operator from Bergman type spaces to Bers spaces, Integral Transforms Spec. Funct. 18 (2007), no. 3-4, 223-231. https://doi.org/10.1080/10652460701210250
  39. X. Zhu, Generalized weighted composition operators from Bloch-type spaces to weighted Bergman spaces, Indian J. Math. 49 (2007), no. 2, 139-149.
  40. X. Zhu, Weighted composition operators from F(p, q, s) spaces to $H^{\infty}_\mu$ spaces, Abstr. Appl. Anal. 2009 (2009), Article ID 290978.
  41. X. Zhu, Generalized weighted composition operators on weighted Bergman spaces, Numer. Funct. Anal. Optim. 30 (2009), no. 7-8, 881-893. https://doi.org/10.1080/01630560903123163
  42. X. Zhu, Weighted composition operators from area Nevalinna spaces into Bloch spaces, Appl. Math. Comput. 215 (2010), no. 12, 4340-4346. https://doi.org/10.1016/j.amc.2009.12.064
  43. X. Zhu, Generalized weighted composition operators on Bloch-type spaces, Ars. Combin. to appear.

피인용 문헌

  1. Product-type operators from Zygmund spaces to Bloch-Orlicz spaces vol.62, pp.11, 2017, https://doi.org/10.1080/17476933.2016.1278436
  2. On a product operator from weighted Bergman-Nevanlinna spaces to weighted Zygmund spaces vol.2014, pp.1, 2014, https://doi.org/10.1186/1029-242X-2014-404
  3. On some product-type operators from Hardy–Orlicz and Bergman–Orlicz spaces to weighted-type spaces vol.233, 2014, https://doi.org/10.1016/j.amc.2014.01.002
  4. On a product-type operator from weighted Bergman–Orlicz space to some weighted type spaces vol.256, 2015, https://doi.org/10.1016/j.amc.2015.01.025
  5. Essential norm of some extensions of the generalized composition operators between kth weighted-type spaces vol.2017, pp.1, 2017, https://doi.org/10.1186/s13660-017-1493-x
  6. PRODUCT-TYPE OPERATORS FROM WEIGHTED BERGMAN-ORLICZ SPACES TO WEIGHTED ZYGMUND SPACES vol.52, pp.4, 2015, https://doi.org/10.4134/BKMS.2015.52.4.1383
  7. Generalized product-type operators from weighted Bergman–Orlicz spaces to Bloch–Orlicz spaces vol.268, 2015, https://doi.org/10.1016/j.amc.2015.06.100
  8. Generalized weighted composition operators from Zygmund spaces to Bloch–Orlicz type spaces vol.273, 2016, https://doi.org/10.1016/j.amc.2015.09.055
  9. A New Characterization of Generalized Weighted Composition Operators from the Bloch Space into the Zygmund Space vol.2013, 2013, https://doi.org/10.1155/2013/925901