Research article

Intertwining relations for composition operators and integral-type operators between the Bloch-type spaces

  • Received: 09 June 2022 Revised: 17 August 2022 Accepted: 18 August 2022 Published: 23 August 2022
  • MSC : 47B38, 47B33, 32H02

  • In this paper, the compact intertwining relations of integral-type operators and composition operators between the Bloch-type spaces are investigated.

    Citation: Hang Zhou. Intertwining relations for composition operators and integral-type operators between the Bloch-type spaces[J]. AIMS Mathematics, 2022, 7(10): 18729-18745. doi: 10.3934/math.20221030

    Related Papers:

  • In this paper, the compact intertwining relations of integral-type operators and composition operators between the Bloch-type spaces are investigated.



    加载中


    [1] A. Biswas, A. Lambert, S. Petrovic, Extended eigenvalues and the Volterra operator, Glasg. Math. J., 44 (2002), 521–534. https://doi.org/10.1017/S001708950203015X doi: 10.1017/S001708950203015X
    [2] P. S. Bourdon, J. H. Shapiro, Intertwining relations and extended eigenvalues for analytic Toeplitz operators, Illinois J. Math., 52 (2008), 1007–1030. https://doi.org/10.1215/ijm/1254403728 doi: 10.1215/ijm/1254403728
    [3] R. E. Castillo, D. D. Clahane, J. F. Farías-López, J. C. Ramos-Fern$\acute{a}$ndez, Composition operators from logarithmic Bloch spaces to weighted Bloch spaces, Appl. Math. Comput., 219 (2013), 6692–6706. https://doi.org/10.1016/j.amc.2012.11.091 doi: 10.1016/j.amc.2012.11.091
    [4] C. C. Cowen, B. D. Maccluer, Composition operators on spaces of analytic functions, CRC Press, 1995.
    [5] S. Li, S. Stevi$\acute{c}$, Generalized composition operators on Zygmund spaces and Bloch type spaces, J. Math. Anal. Appl., 338 (2008), 1282–1295. https://doi.org/10.1016/j.jmaa.2007.06.013 doi: 10.1016/j.jmaa.2007.06.013
    [6] S. Li, S. Stevi$\acute{c}$, Riemann-Stieltjes type integral operators on the unit ball in ${\mathbb C}^n$, Complex Var. Elliptic Equ., 52 (2007), 495–517. https://doi.org/10.1080/17476930701235225 doi: 10.1080/17476930701235225
    [7] X. S. Li, S. Stević, Products of integral-type operators and composition operators between Bloch-type spaces, J. Math. Anal. Appl., 349 (2009), 596–610. https://doi.org/10.1016/j.jmaa.2008.09.014 doi: 10.1016/j.jmaa.2008.09.014
    [8] Y. Liu, Y. Yu, On a Li-Stević integral-type operator from Bloch-type spaces into logarithmic Bloch spaces, Integr. Transf. Spec. F., 21 (2010), 93–103. https://doi.org/10.1080/10652460903047468 doi: 10.1080/10652460903047468
    [9] Y. X. Liang, Z. H. Zhou, The Products of differentiation and composition operators from logarithmic Bloch spaces to mu-Bloch Spaces, B. Iran. Math. Soc., 46 (2020), 159–176. https://doi.org/10.1007/s41980-019-00248-w doi: 10.1007/s41980-019-00248-w
    [10] S. Ohno, K. Stroethoff, R. H. Zhao, Weighted composition operators between Bloch type spaces, Rocky MT J. Math., 33 (2003), 191–215. https://doi.org/10.1216/rmjm/1181069993 doi: 10.1216/rmjm/1181069993
    [11] J. C. Ramos-Fernández, Logarithmic Bloch spaces and their weighted composition operators, Rend. Circ. Mat. Palerm., 65 (2016), 159–174. https://doi.org/10.1007/s12215-015-0226-6 doi: 10.1007/s12215-015-0226-6
    [12] S. Stević, R. P. Agarwal, Weighted composition operators from logarithmic Bloch-type spaces to Bloch-type spaces, J. Inequal. Appl., 2009, 964814. https://doi.org/10.1155/2009/964814 doi: 10.1155/2009/964814
    [13] S. Stević, On new Bloch-type spaces, Appl. Math. Comput., 215 (2009), 841–849. https://doi.org/10.1016/j.amc.2009.06.009 doi: 10.1016/j.amc.2009.06.009
    [14] S. Stević, On an integral-type operator from logarithmic Bloch-type and mixed-norm spaces to Bloch-type spaces, Nonlinear Anal.-Theor., 71 (2009), 6323–6342. https://doi.org/10.1016/j.na.2009.06.087 doi: 10.1016/j.na.2009.06.087
    [15] S. Stević, Norm and essential norm of an integral-type operator from the logarithmic Bloch space to the Bloch-type space on the unit ball, Math. Method. Appl. Sci., 2022, 1–11. https://doi.org/10.1002/mma.8487 doi: 10.1002/mma.8487
    [16] S. Stević, Z. J. Jiang, Weighted iterated radial composition operators from logarithmic Bloch spaces to weighted-type spaces on the unit ball, Math. Method. Appl. Sci., 45 (2022), 3083–3097. https://doi.org/10.1002/mma.7978 doi: 10.1002/mma.7978
    [17] S. Stević, On an integral-type operator from logarithmic Bloch-type spaces to mixed-norm spaces on the unit ball, Appl. Math. Comput., 215 (2010), 3817–3823. https://doi.org/10.1016/j.amc.2009.11.022 doi: 10.1016/j.amc.2009.11.022
    [18] S. Stević, On operator $P_\varphi^g$ from the logarithmic Bloch-type space to the mixed-norm space on unit ball, Appl. Math. Comput., 215 (2010), 4248–4255. https://doi.org/10.1016/j.amc.2009.12.048 doi: 10.1016/j.amc.2009.12.048
    [19] S. Stević, Weighted composition operators from the logarithmic weighted-type space to the weighted Bergman space in $\mathbb{C}^n$, Appl. Math. Comput., 216 (2010), 924–928.
    [20] S. Stević, Norm of some operators from logarithmic Bloch-type spaces to weighted-type spaces, Appl. Math. Comput., 218 (2012), 11163–11170. https://doi.org/10.1016/j.amc.2012.04.073 doi: 10.1016/j.amc.2012.04.073
    [21] C. Z. Tong, Z. H. Zhou, Compact intertwining relations for composition operators between the weighted Bergman spaces and the weighted Bloch spaces, J. Korean Math. Soc., 51 (2014), 125–135. https://doi.org/10.4134/JKMS.2014.51.1.125 doi: 10.4134/JKMS.2014.51.1.125
    [22] C. Z. Tong, Z. H. Zhou, Intertwining relations for Volterra operators on the Bergman space, Illinois J. Math., 57 (2013), 195–211. https://doi.org/10.1215/ijm/1403534492 doi: 10.1215/ijm/1403534492
    [23] C. Z. Tong, C. Yuan, Z. H. Zhou, Compact intertwining relations for composition operators on H$^\infty$ and the Bloch spaces, New York J. Math., 24 (2018), 611–629.
    [24] K. Zhu, Spaces of holomorphic functions in the unit ball, Graduate Texts in Mathematics 226, Springer, New York, 2005.
    [25] Z. H. Zhou, L. Zhang, H. G. Zeng, Essential commutativity of some integral and composition operators, Bull. Aust. Math. Soc., 85 (2012), 143–153. https://doi.org/10.1017/S0004972711002723 doi: 10.1017/S0004972711002723
  • Reader Comments
  • © 2022 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(1094) PDF downloads(51) Cited by(0)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog