Research article Special Issues

Differences weighted composition operators in several variables between some spaces of analytic functions

  • Received: 29 July 2023 Revised: 12 September 2023 Accepted: 19 September 2023 Published: 26 September 2023
  • MSC : 47B91

  • The boundedness and compactness of weighted composition operators have been extensively investigated on various analytic function spaces. In this paper, we study the boundedness and compactness of two several variables differences weighted composition operators on some analytic function spaces.

    Citation: Aydah Mohammed Ayed Al-Ahmadi. Differences weighted composition operators in several variables between some spaces of analytic functions[J]. AIMS Mathematics, 2023, 8(11): 27363-27375. doi: 10.3934/math.20231400

    Related Papers:

  • The boundedness and compactness of weighted composition operators have been extensively investigated on various analytic function spaces. In this paper, we study the boundedness and compactness of two several variables differences weighted composition operators on some analytic function spaces.



    加载中


    [1] R. F. Allen, F. Colonna, Weighted composition operators from ${\bf{H}}_\alpha$ to the Bloch space of a bounded homogeneous domain, Integr. Equat. Oper. Th., 66 (2010), 21–40. https://doi.org/10.1007/s00020-009-1736-4 doi: 10.1007/s00020-009-1736-4
    [2] J. Bonet, M. Lindstrom, E. Wolf, Differences of composition operators between weighted Banach spaces of holomorphic functions, J. Aust. Math. Soc., 84 (2008), 9–20. https://doi.org/10.1017/S144678870800013X doi: 10.1017/S144678870800013X
    [3] B. S. Bourdon, J. A. Cima, A. L. Matheson, Compact composition operators on BMOA, T. Am. Math. Soc. 351 (1999), 2183–2169.
    [4] B. Choe, H. Koo, I. Park, Compact differences of composition operators over polydisks, Integr. Equat. Oper. Th., 73 (2013), 57–91. https://doi.org/10.1007/s00020-012-1962-z doi: 10.1007/s00020-012-1962-z
    [5] C. Cowen, B. Maccluer, Composition operators on spaces of analytic functions, Boca Raton: CRC Press, 1995.
    [6] X. Fu, Differences of weighetd composition operator from weighted Bergman spaces to weighted-type spaces, Bull. Math. Anal. Appl., 5 (2013), 65–70.
    [7] A. E. S. Ahmed, M. A. Bakhit, Holomorphic ${{\mathcal N}_K}$ and Bergman-type spaces, Birkhuser Series on Operator Theory: Advances and Applications, Basel: BirkhuserVerlag Publisher, 195 (2009), 121–138. https://doi.org/10.1007/978-3-0346-0174-0-5
    [8] A. E. S. Ahmed, M. A. Bakhit, Hadamard products and ${\mathcal N}_K$ spaces, Math. Comput. Model., 51 (2010), 33–43. https://doi.org/10.1016/j.mcm.2009.08.037 doi: 10.1016/j.mcm.2009.08.037
    [9] K. Heller, B. D. Maccluer, R. J. Weir, Compact differences of composition operators in several variables, Integr. Equat. Oper. Th., 69 (2011), 419–428. https://doi.org/10.1007/s00020-010-1840-5 doi: 10.1007/s00020-010-1840-5
    [10] T. Hosokawa, S. Ohno, Differences of weighted composition operators from $H^\infty$ to Bloch space, Taiwan. J. Math., 16 (2012), 2093–2105. https://doi.org/10.11650/twjm/1500406842 doi: 10.11650/twjm/1500406842
    [11] T. Hosokawa, Differences of weighted composition operators on the Bloch spaces, Complex Anal. Oper. Th., 3 (2009), 847–866. https://doi.org/10.1007/s11785-008-0062-1 doi: 10.1007/s11785-008-0062-1
    [12] T. Hosokawa, S. Ohno, Differences of composition operators on the Bloch spaces, J. Operat. Theor., 57 (2007), 229–242.
    [13] L. Jiang, C. Ouyang, Compact differences of composition operators on holomorphic function spaces in the unit ball, Acta Math. Sci., 31 (2011), 1679–1693. https://doi.org/10.1016/S0252-9602(11)60291-9 doi: 10.1016/S0252-9602(11)60291-9
    [14] B. Hu, L. H. Khoi, Compact difference of weighted composition operators on ${\mathcal N}_p$ spaces in the ball, Roum. J. Pure Appl. Math., 60 (2015), 101–116.
    [15] A. E. Shammahy, Weighted composition operators acting between kind of weighted Bergman-type spaces and the Bers-type space, Inter. J. Math. Comput. Phys. Electr. Comput. Eng., 8 (2014), 496–499.
    [16] M. Lindstrom, E. Wolf, Essential norm of the difference of weighted composition operators, Monatsh. Math., 153 (2000), 133–143. https://doi.org/10.1007/s00605-007-0493-1 doi: 10.1007/s00605-007-0493-1
    [17] P. J. Nieminen, Compact differences of composition operators on Bloch and Lipschitz spaces, Comput. Meth. Funct. Th., 7 (2007), 325–344. https://doi.org/10.1007/BF03321648 doi: 10.1007/BF03321648
    [18] C. Shaolin, H. Hidetaka, Z. J. Feng, Composition operators on Bloch and Hardy type spaces, Math. Z., 301 (2022), 3939–3957. https://doi.org/10.1007/s00209-022-03046-z doi: 10.1007/s00209-022-03046-z
    [19] C. Shaolin, H. Hidetaka, Harmonic Lipschitz type spaces and composition operators meet majorants, J. Geom. Anal., 33 (2023), 181. https://doi.org/10.1007/s12220-023-01232-x doi: 10.1007/s12220-023-01232-x
    [20] J. H. Shapiro, Composition operators and classical function theory, New York: Springer-Verlag, 1993. https://doi.org/10.1007/978-1-4612-0887-7
    [21] R. Zhao, On $\alpha$-Bloch functions and VMOA, Acta Math. Sci., 3 (1996), 349–360. https://doi.org/10.1016/S0252-9602(17)30811-1 doi: 10.1016/S0252-9602(17)30811-1
    [22] K. Zhu, Operator theory in function spaces, New York: Marcel Dekker, 2007. https://doi.org/10.1090/surv/138
    [23] X. Zhua, W. Yang, Differences of composition operators from weighted Bergman spaces to Bloch spaces, Filomat, 28 (2014), 1935–1941. https://doi.org/10.2298/FIL1409935Z doi: 10.2298/FIL1409935Z
    [24] S. Ueki, Weighted composition operators acting between the ${\mathcal N}_p$-space and the Weighted-type space ${\mathcal H}_\alpha^\infty$, Indagat. Math., 23 (2012), 243–255. https://doi.org/10.1016/j.indag.2011.11.006 doi: 10.1016/j.indag.2011.11.006
    [25] E. Wolf, Weighted composition operators between weighted Bloch type spaces, B. Soc. Royale Sci. Liège, 80 (2011), 806–816.
  • Reader Comments
  • © 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(733) PDF downloads(54) Cited by(1)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog