New characterizations for differences of composition operators between weighted-type spaces in the unit ball

C. Chen

doi:10.37863/umzh.v73i8.607

C. Chen Tianjin Univ. Finance and Economics, China

DOI: https://doi.org/10.37863/umzh.v73i8.607

Анотація

Запропоновано асимптотично еквівалентні вирази для суттєвої норми різниць операторів композиції, які діють у вагових просторах голоморфних функцій в одиничній кулі з $\mathbb{C}^N.$ Зокрема, наведено опис у термінах $\langle z, \zeta\rangle^m,$ з якого безпосередньо випливають необхідні та достатні умови компактності. Крім того, охарактеризовано обмеженість цих операторів.

Посилання

J. Bonet, P. Domanski, M. Lindström, Essential norm and weak compactness of composition operators on weithted Banach spaces of analytic functions, Canad. Math. Bull., 42, № 2, 139 – 148 (1995), https://doi.org/10.4153/CMB-1999-016-x DOI: https://doi.org/10.4153/CMB-1999-016-x

J. Bonet, M. Lindström, E. Wolf, Difference of composition operators between weighted Banach spaces of holomorphic functions, J. Aust. Math. Soc., 84, 9 – 20 (2008), https://doi.org/10.1017/S144678870800013X DOI: https://doi.org/10.1017/S144678870800013X

C. Chen, Z. H. Zhou, Essential norms of generalized composition operators between Bloch-type spaces in the unit ball, Complex Var. and Elliptic Equat., 60, № 5, 696 – 706 (2015), https://doi.org/10.1080/17476933.2014.968848 DOI: https://doi.org/10.1080/17476933.2014.968848

C. Chen, Z. H. Zhou, Essential norms of the integral-type composition operators between Bloch-type spaces, Integr. Trans. Spec. F. (2014); http://dx.doi.org/10.1080/10652469.2014.887073 DOI: https://doi.org/10.1080/10652469.2014.887073

J. N. Dai, Compact composition operators on the Bloch space of the unit ball, J. Math. Anal. and Appl., 386, 294 – 299 (2012), https://doi.org/10.1016/j.jmaa.2011.07.067 DOI: https://doi.org/10.1016/j.jmaa.2011.07.067

J. N. Dai, C. H. Ouyang, Differences of weighted composition operators on $H^infty_alpha(B_N)^ast$, J. Inequal. and Appl., Article ID 127431 (2009), 19 p., https://doi.org/10.1155/2009/127431 DOI: https://doi.org/10.1155/2009/127431

Z. S. Fang, Z. H. Zhou, Essential norms of composition operators between Bloch type spaces in the polydisk, Arch. Math., 99, 547 – 556 (2012). DOI: https://doi.org/10.1007/s00013-012-0457-0

Z. S. Fang, Z. H. Zhou, New characterizations of the weighted composition operators between Bloch type spaces in the polydisk, Canad. Math. Bull. (2013); http://dx.doi.org/10.4153/CMB-2013-043-4 DOI: https://doi.org/10.4153/CMB-2013-043-4

T. Hosokawa, K. Izuchi, S. Ohno, Topological structure of weighted composition operators on $H^{infty}$ , Integral Equat. Oper. Theory, 53, 509 – 526 (2005), https://doi.org/10.1007/s00020-004-1337-1 DOI: https://doi.org/10.1007/s00020-004-1337-1

O. Hyvarinen, M. Lindström, Estimates of essential norms of weighted composition operators between Bloch-type spaces, J. Math. Anal. and Appl., 393, 38 – 44 (2012), https://doi.org/10.1016/j.jmaa.2012.03.059 DOI: https://doi.org/10.1016/j.jmaa.2012.03.059

Y. X. Liang, C. Chen, New characterizations for differences of Volterra-type operators from $alpha$ -weighted-type space to $beta$ -Bloch – Orlicz space, Math. Nachr., 291, № 14-15, 2298 – 2317 (2018), https://doi.org/10.1002/mana.201700151 DOI: https://doi.org/10.1002/mana.201700151

Y. X. Liang, Z. H. Zhou, Differences of integral-type operators from weighted Bergman spaces to $beta$ -Bloch – Orlicz spaces, Publ. Math. Debrecen, 92, № 3-4, 381 – 410 (2018), https://doi.org/10.5486/pmd.2018.7929 DOI: https://doi.org/10.5486/PMD.2018.7929

Y. X. Liang, Z. H. Zhou, New estimate of essential norm of composition followed by differentiation between Bloch-type spces, Banach J. Math. Anal., 8, 118 – 137 (2014). DOI: https://doi.org/10.15352/bjma/1381782092

Y. X. Liang, Z. H. Zhou, Essential norm of product of differentiation and composition operators between Bloch-type spaces, Arch. Math., 100, № 4, 347 – 360 (2013), https://doi.org/10.1007/s00013-013-0499-y DOI: https://doi.org/10.1007/s00013-013-0499-y

M. Lindström, E. Wolf, Essential norm of the difference of weighted composition operators, Monatsh. Math., 153, 133 – 143 (2008), https://doi.org/10.1007/s00605-007-0493-1 DOI: https://doi.org/10.1007/s00605-007-0493-1

Y. C. Shi, S. X. Li, Differences of composition operators on Bloch type spaces, Complex Anal. and Oper. Theory, 11, 227 – 242 (2017), https://doi.org/10.1007/s11785-016-0595-7 DOI: https://doi.org/10.1007/s11785-016-0595-7

S. Stevic, Essential norm of differences of weighted composition operators between weighted-type spaces on the unit ball, Appl. Math. and Comput., 217, 1811 – 1824 (2010), https://doi.org/10.1016/j.amc.2010.02.034 DOI: https://doi.org/10.1016/j.amc.2010.02.034

H. Wulan, D. Zheng, K. Zhu, Compact composition operators on BMOA and the Bloch space, Proc. Amer. Math. Soc., 137, 3861 – 3868 (2009), https://doi.org/10.1090/S0002-9939-09-09961-4 DOI: https://doi.org/10.1090/S0002-9939-09-09961-4

R. Zhao, Essential norms of composition operators between Bloch type spaces, Proc. Amer. Math. Soc., 138, 2537 – 2546 (2010), https://doi.org/10.1090/S0002-9939-10-10285-8 DOI: https://doi.org/10.1090/S0002-9939-10-10285-8

Z. H. Zhou, Y. Liu, The essential norms of composition operators between generalized Bloch spaces in the polydisk and their applications, J. Inequal. and Appl., 2006, Article ID 90742 (2006), 22 p., https://doi.org/10.1155/JIA/2006/90742 DOI: https://doi.org/10.1155/JIA/2006/90742