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http://dx.doi.org/10.4134/BKMS.b200464

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.4, 2021 , pp. 815-828 More about this Journal
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
Volterra type operator; Morrey type space; weighted BMOA space;
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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   DOI
2 P. L. Duren, Theory of Hp Spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York, 1970.
3 J. B. Garnett, Bounded Analytic Functions, Pure and Applied Mathematics, 96, Academic Press, Inc., New York, 1981.
4 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   DOI
5 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   DOI
6 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   DOI
7 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   DOI
8 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   DOI
9 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   DOI
10 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   DOI
11 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   DOI
12 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.
13 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   DOI
14 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   DOI
15 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   DOI
16 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   DOI
17 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   DOI
18 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   DOI
19 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   DOI
20 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   DOI
21 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
22 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   DOI
23 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   DOI
24 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   DOI
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