대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제57권3호
  • /
  • Pages.583-595
  • /
  • 2020
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

WEIGHTED COMPOSITION OPERATORS ON BERS-TYPE SPACES OF LOO-KENG HUA DOMAINS

  • Jiang, Zhi-jie (School of Mathematics and Statistics Sichuan University of Science and Engineering) ;
  • Li, Zuo-an (School of Mathematics and Statistics Sichuan University of Science and Engineering)
  • 투고 : 2019.02.25
  • 심사 : 2020.01.17
  • 발행 : 2020.05.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Let HEI, HEII, HEIII and HEIV be the first, second, third and fourth type Loo-Keng Hua domain respectively, 𝜑 a holomorphic self-map of HEI, HEII, HEIII, or HEIV and u ∈ H(𝓜) the space of all holomorphic functions on 𝓜 ∈ {HEI, HEII, HEIII, HEIV}. In this paper, motivated by the well known Hua's matrix inequality, first some inequalities for the points in the Bers-type spaces of the Loo-Keng Hua domains are obtained, and then the boundedness and compactness of the weighted composition operators W𝜑,u : f ↦ u · f ◦ 𝜑 on Bers-type spaces of these domains are characterized.

키워드

참고문헌

  1. R. F. Allen and F. Colonna, Weighted composition operators on the Bloch space of a bounded homogeneous domain, in Topics in operator theory. Volume 1. Operators, matrices and analytic functions, 11-37, Oper. Theory Adv. Appl., 202, Birkhauser Verlag, Basel, 2010. https://doi.org/10.1007/978-3-0346-0158-0_2
  2. R. F. Allen and F. Colonna, Weighted composition operators from H1 to the Bloch space of a bounded homogeneous domain, Integral Equations Operator Theory 66 (2010), no. 1, 21-40. https://doi.org/10.1007/s00020-009-1736-4
  3. F. Colonna and S. Li, Weighted composition operators from the minimal Mobius invariant space into the Bloch space, Mediterr. J. Math. 10 (2013), no. 1, 395-409. https://doi.org/10.1007/s00009-012-0182-8
  4. C. C. Cowen and B. D. MacCluer, Composition operators on spaces of analytic functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1995.
  5. K. Esmaeili and M. Lindstrom, Weighted composition operators between Zygmund type spaces and their essential norms, Integral Equations Operator Theory 75 (2013), no. 4, 473-490.http://doi.org/10.1007/s00020-013-2038-4
  6. W. He and L. Jiang, Composition operator on Bers-type spaces, Acta Math. Sci. Ser. B (Engl. Ed.) 22 (2002), no. 3, 404-412. https://doi.org/10.1016/S0252-9602(17)30310-7
  7. L. Jiang and Y. Li, Bers-type spaces and composition operators, Northeast. Math. J. 18 (2002), no. 3, 223-232. https://doi.org/10.3969/j.issn.1674-5647.2002.03.005
  8. Z. Jiang, Composition operators from weighted Bergman spaces to some spaces of analytic functions on the upper half-plane, Util. Math. 93 (2014), 205-212.
  9. Z. Jiang, On a product-type operator from weighted Bergman-Orlicz space to some weighted type spaces, Appl. Math. Comput. 256 (2015), 37-51. https://doi.org/10.1016/j.amc.2015.01.025
  10. A. S. Kucik, Weighted composition operators on spaces of analytic functions on the complex half-plane, Complex Anal. Oper. Theory 12 (2018), no. 8, 1817-1833. https://doi.org/10.1007/s11785-017-0677-1
  11. 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
  12. S. Li and S. Stevic, Weighted composition operators from H1 to the Bloch space on the polydisc, Abstr. Appl. Anal. 2007 (2007), Art. ID 48478, 13 pp. https://doi.org/10.1155/2007/48478
  13. L. Luo and S. Ueki, Weighted composition operators between weighted Bergman spaces and Hardy spaces on the unit ball of ${\mathbb{C}}^n$, J. Math. Anal. Appl. 326 (2007), no. 1, 88-100. https://doi.org/10.1016/j.jmaa.2006.02.038
  14. 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
  15. S. Stevic, Essential norms of weighted composition operators from the ${\alpha}$-Bloch space to a weighted-type space on the unit ball, Abstr. Appl. Anal. 2008 (2008), Art. ID 279691, 11 pp. https://doi.org/10.1155/2008/279691
  16. S. Stevic, Norm of weighted composition operators from Bloch space to $H_{\mu}^{\infty}$ on the unit ball, Ars Combin. 88 (2008), 125-127.
  17. 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
  18. S. Stevic, Weighted composition operators from Bergman-Privalov-type spaces to weighted-type spaces on the unit ball, Appl. Math. Comput. 217 (2010), no. 5, 1939-1943. https://doi.org/10.1016/j.amc.2010.06.049
  19. S. Stevic, R. Chen, and Z. Zhou, Weighted composition operators between Bloch type spaces in the polydisc, Sb. Math. 201 (2010), no. 1-2, 289-319; translated from Mat. Sb. 201 (2010), no. 2, 131-160. https://doi.org/10.1070/SM2010v201n02ABEH004073
  20. S. Stevic and Zh. J. Jiang, Differences of weighted composition operators on the unit polydisk, Sib. Math. J. 52 (2011), no. 2, 358-371; translated from Sibirsk. Mat. Zh. 52 (2011), no. 2, 454-468. https://doi.org/10.1134/S0037446611020200
  21. S. Stevic and A. K. Sharma, Weighted composition operators between growth spaces of the upper half-plane, Util. Math. 84 (2011), 265-272.
  22. S. Stevic and A. K. Sharma, Weighted composition operators between Hardy and growth spaces on the upper half-plane, Appl. Math. Comput. 217 (2011), no. 10, 4928-4934. https://doi.org/10.1016/j.amc.2010.11.041
  23. W. Yin, The Bergman kernels on super-Cartan domains of the first type, Sci. China Ser. A 43 (2000), no. 1, 13-21. https://doi.org/10.1007/BF02903843
  24. W. Yin, A. Wang, Zh. G. Zhao, and B. X. Guan, Computations of Bergman kernels on Hua domains, Adv. Math. (China) 30 (2001), no. 2, 185-188. https://doi.org/10.3969/j.issn.1000-0917.2001.02.014
  25. K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Graduate Texts in Mathematics, 226, Springer-Verlag, New York, 2005.