Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

INTEGRAL OPERATORS FROM MORREY TYPE SPACES TO WEIGHTED BMOA SPACES

  • Qian, Ruishen (School of Mathematics and Statistics Lingnan Normal University) ;
  • Zhu, Xiangling (University of Electronic Science and Technology of China Zhongshan Institute)
  • Received : 2020.05.25
  • Accepted : 2021.04.28
  • Published : 2021.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

Under some mild conditions for the weight function K, the boundedness, compactness and essential norm of integral operators Tg and Ig from Morrey type spaces HpK to weighted BMOA spaces $BMOAK_{K,{\frac{2}{p}}}$ investigated in this paper.

Keywords

Acknowledgement

This work was supported by NNSF of China (No.11801250) and (No.11871257), Overseas Scholarship Program for Elite Young and Middle-aged Teachers of Lingnan Normal University, Yanling Youqing Program of Lingnan Normal University (No.YL20200202), Lingnan Normal University (No.LZ1905), and the Innovation and developing School Project of Guangdong Province (No. 2019KZDXM032).

References

  1. A. Aleman and J. A. Cima, An integral operator on Hp and Hardy's inequality, J. Anal. Math. 85 (2001), 157-176. https://doi.org/10.1007/BF02788078
  2. A. Aleman and A. G. Siskakis, An integral operator on Hp, Complex Variables Theory Appl. 28 (1995), no. 2, 149-158. https://doi.org/10.1080/17476939508814844
  3. A. Aleman and A. G. Siskakis, Integration operators on Bergman spaces, Indiana Univ. Math. J. 46 (1997), no. 2, 337-356. https://doi.org/10.1512/iumj.1997.46.1373
  4. P. L. Duren, Theory of Hp Spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York, 1970.
  5. M. Essen, H. Wulan, and J. Xiao, Several function-theoretic characterizations of Mobius invariant QK spaces, J. Funct. Anal. 230 (2006), no. 1, 78-115. https://doi.org/10.1016/j.jfa.2005.07.004
  6. J. B. Garnett, Bounded Analytic Functions, Pure and Applied Mathematics, 96, Academic Press, Inc., New York, 1981.
  7. D. Girela and J. Pelaez, Carleson measures, multipliers and integration operators for spaces of Dirichlet type, J. Funct. Anal. 241 (2006), no. 1, 334-358. https://doi.org/10.1016/j.jfa.2006.04.025
  8. J. Laitila, S. Miihkinen, and P. J. Nieminen, Essential norms and weak compactness of integration operators, Arch. Math. (Basel) 97 (2011), no. 1, 39-48. https://doi.org/10.1007/s00013-011-0272-z
  9. P. Li, J. Liu, and Z. Lou, Integral operators on analytic Morrey spaces, Sci. China Math. 57 (2014), no. 9, 1961-1974. https://doi.org/10.1007/s11425-014-4811-5
  10. S. Li, J. Liu, and C. Yuan, Embedding theorems for Dirichlet type spaces, Canad. Math. Bull. 63 (2020), no. 1, 106-117. https://doi.org/10.4153/s0008439519000201
  11. S. Li and S. Stevic, Volterra-type operators on Zygmund spaces, J. Inequal. Appl. 2007 (2007), Art. ID 32124, 10 pp. https://doi.org/10.1155/2007/32124
  12. S. Li and S. Stevic, Riemann-Stieltjes operators between α-Bloch spaces and Besov spaces, Math. Nachr. 282 (2009), no. 6, 899-911. https://doi.org/10.1002/mana.200610778
  13. S. Li and H. Wulan, Volterra type operators on QK spaces, Taiwanese J. Math. 14 (2010), no. 1, 195-211. https://doi.org/10.11650/twjm/1500405735
  14. J. Liu and Z. Lou, Carleson measure for analytic Morrey spaces, Nonlinear Anal. 125 (2015), 423-432. https://doi.org/10.1016/j.na.2015.05.016
  15. J. Liu and Z. Lou, Properties of analytic Morrey spaces and applications, Math. Nachr. 288 (2015), no. 14-15, 1673-1693. https://doi.org/10.1002/mana.201300301
  16. Ch. Pommerenke, Schlichte Funktionen und analytische Funktionen von beschrankter mittlerer Oszillation, Comment. Math. Helv. 52 (1977), no. 4, 591-602. https://doi.org/10.1007/BF02567392
  17. R. Qian and S. Li, Volterra type operators on Morrey type spaces, Math. Inequal. Appl. 18 (2015), no. 4, 1589-1599. https://doi.org/10.7153/mia-18-122
  18. Y. Shi and S. Li, Essential norm of integral operators on Morrey type spaces, Math. Inequal. Appl. 19 (2016), no. 1, 385-393. https://doi.org/10.7153/mia-19-30
  19. A. G. Siskakis and R. Zhao, A Volterra type operator on spaces of analytic functions, in Function spaces (Edwardsville, IL, 1998), 299-311, Contemp. Math., 232, Amer. Math. Soc., Providence, RI, 1999. https://doi.org/10.1090/conm/232/03406
  20. J. Wang, The Carleson measure problem between analytic Morrey spaces, Canad. Math. Bull. 59 (2016), no. 4, 878-890. https://doi.org/10.4153/CMB-2016-013-9
  21. Z. Wu and C. Xie, Q spaces and Morrey spaces, J. Funct. Anal. 201 (2003), no. 1, 282-297. https://doi.org/10.1016/S0022-1236(03)00020-X
  22. H. Wulan and J. Zhou, QK and Morrey type spaces, Ann. Acad. Sci. Fenn. Math. 38 (2013), no. 1, 193-207. https://doi.org/10.5186/aasfm.2013.3801
  23. S. Ye and Z. Lou, Cyclic vectors and cellular indecomposable operators on Qp spaces, Acta Math. Sci. Ser. B (Engl. Ed.) 31 (2011), no. 2, 434-440. https://doi.org/10.1016/S0252-9602(11)60243-9
  24. J. Z. Zhou and S. X. Li, Characterization and Carleson measure for analytic Morrey type spaces, Acta Math. Sinica (Chin. Ser.) 59 (2016), no. 5, 577-584.
  25. K. Zhu, Operator Theory in Function Spaces, second edition, Mathematical Surveys and Monographs, 138, American Mathematical Society, Providence, RI, 2007. https://doi.org/10.1090/surv/138