×
Liang, Yu-Xia; Zhou, Ze-Hua

Product of extended Cesàro operator and composition operator from Lipschitz space to \(F(p,q,s)\) space on the unit ball. (English) Zbl 1221.47058

Abstr. Appl. Anal. 2011, Article ID 152635, 9 p. (2011).
Summary: This paper characterizes the boundedness and compactness of the product of an extended Cesàro operator and a composition operator from Lipschitz space to \(F(p,q,s)\) space on the unit ball of \(\mathbb C^n\).

Cited in 3 Documents

MSC:

47B38 Linear operators on function spaces (general)

Keywords:

boundedness; compactness; product of operators; Lipschitz space
PDF BibTeX XML Cite
\textit{Y.-X. Liang} and \textit{Z.-H. Zhou}, Abstr. Appl. Anal. 2011, Article ID 152635, 9 p. (2011; Zbl 1221.47058)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] W. Rudin, Function Theory in the Unit Ball of \Bbb Cn, vol. 241 of Fundamental Principles of Mathematical Science, Springer, Berlin, Germany, 1980. · Zbl 0495.32001
[2] K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, vol. 226 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 2005. · Zbl 1067.32005
[3] S. Li and S. Stević, “Compactness of Riemann-Stieltjes operators between F(p, q, s) spaces and \alpha -Bloch spaces,” Publicationes Mathematicae Debrecen, vol. 72, no. 1-2, pp. 111-128, 2008. · Zbl 1164.47040
[4] Z.-H. Zhou and R.-Y. Chen, “Weighted composition operators from F(p, q, s) to Bloch type spaces on the unit ball,” International Journal of Mathematics, vol. 19, no. 8, pp. 899-926, 2008. · Zbl 1163.47021
[5] H.-G. Zeng and Z.-H. Zhou, “An estimate of the essential norm of a composition operator from F(p, q, s) to \beta \alpha in the unit ball,” journal of Inequalities and Applications, vol. 2010, Article ID 132970, 22 pages, 2010. · Zbl 1191.47033
[6] C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, Fla, USA, 1995. · Zbl 0873.47017
[7] J. H. Shapiro, Composition Operators and Classical Function Theory, Universitext: Tracts in Mathematics, Springer, New York, NY, USA, 1993. · Zbl 0791.30033
[8] Z. Zhou and J. Shi, “Compactness of composition operators on the Bloch space in classical bounded symmetric domains,” The Michigan Mathematical Journal, vol. 50, no. 2, pp. 381-405, 2002. · Zbl 1044.47021
[9] Z. Hu, “Extended Cesàro operators on mixed norm spaces,” Proceedings of the American Mathematical Society, vol. 131, no. 7, pp. 2171-2179, 2003. · Zbl 1054.47023
[10] K. Avetisyan and S. Stević, “Extended Cesàro operators between different Hardy spaces,” Applied Mathematics and Computation, vol. 207, no. 2, pp. 346-350, 2009. · Zbl 1163.32004
[11] Z.-S. Fang and Z.-H. Zhou, “Extended Cesáro operators on BMOA spaces in the unit ball,” Journal of Mathematical Inequalities, vol. 4, no. 1, pp. 27-36, 2010. · Zbl 1185.47032
[12] Z.-S. Fang and Z.-H. Zhou, “Extended Cesàro operators from generally weighted Bloch spaces to Zygmund space,” Journal of Mathematical Analysis and Applications, vol. 359, no. 2, pp. 499-507, 2009. · Zbl 1170.32003
[13] Z.-S. Fang and Z.-H. Zhou, “Extended Cesáro operators on Zygmund spaces in the unit ball,” Journal of Computational Analysis and Applications, vol. 11, no. 3, pp. 406-413, 2009. · Zbl 1181.47031
[14] D. Gu, “Extended Cesàro operators from logarithmic-type spaces to Bloch-type spaces,” Abstract and Applied Analysis, vol. 2009, Article ID 246521, 9 pages, 2009. · Zbl 1168.47028
[15] Z. Hu, “Extended Cesàro operators on Bergman spaces,” Journal of Mathematical Analysis and Applications, vol. 296, no. 2, pp. 435-454, 2004. · Zbl 1072.47029
[16] S. Li and S. Stević, “Riemann-Stieltjes operators on Hardy spaces in the unit ball of \Bbb Cn,” Bulletin of the Belgian Mathematical Society, vol. 14, no. 4, pp. 621-628, 2007. · Zbl 1136.47023
[17] S. Li and S. Stević, “Riemann-Stieltjes-type integral operators on the unit ball in \Bbb Cn,” Complex Variables and Elliptic Equations, vol. 52, no. 6, pp. 495-517, 2007. · Zbl 1124.47022
[18] S. Li and S. Stević, “Riemann-Stieltjes operators between different weighted Bergman spaces,” Bulletin of the Belgian Mathematical Society, vol. 15, no. 4, pp. 677-686, 2008. · Zbl 1169.47026
[19] S. Li and S. Stević, “Cesàro-type operators on some spaces of analytic functions on the unit ball,” Applied Mathematics and Computation, vol. 208, no. 2, pp. 378-388, 2009. · Zbl 1166.45009
[20] J. Xiao, “Riemann-Stieltjes operators on weighted Bloch and Bergman spaces of the unit ball,” Journal of the London Mathematical Society, vol. 70, no. 1, pp. 199-214, 2004. · Zbl 1064.47034
[21] J. Xiao, “Riemann-Stieltjes operators between weighted Bergman spaces,” in Complex and Harmonic Analysis, pp. 205-212, DEStech, Lancaster, UK, 2007. · Zbl 1186.47034
[22] X. Tang, “Extended Cesàro operators between Bloch-type spaces in the unit ball of \Bbb Cn,” Journal of Mathematical Analysis and Applications, vol. 326, no. 2, pp. 1199-1211, 2007. · Zbl 1117.47022
[23] X. Zhu, “Integral-type operators from iterated logarithmic Bloch spaces to Zygmund-type spaces,” Applied Mathematics and Computation, vol. 215, no. 3, pp. 1170-1175, 2009. · Zbl 1185.45021
[24] Z.-H. Zhou and M. Zhu, “Extended Cesáro operators between generalized Besov spaces and Bloch type spaces in the unit ball,” Journal of Function Spaces and Applications, vol. 7, no. 3, pp. 209-223, 2009. · Zbl 1221.47065
[25] S. Li and S. Stević, “Products of Volterra type operator and composition operator from H\infty and Bloch spaces to Zygmund spaces,” Journal of Mathematical Analysis and Applications, vol. 345, no. 1, pp. 40-52, 2008. · Zbl 1145.47022
[26] S. Li and S. Stević, “Products of composition and integral type operators from H\infty to the Bloch space,” Complex Variables and Elliptic Equations, vol. 53, no. 5, pp. 463-474, 2008. · Zbl 1159.47019
[27] H. Y. Li and X. Z. Yang, “Products of integral-type and composition operators from generally weighted Bloch space to F(p, q, s) space,” Faculty of Sciences and Mathematics, vol. 23, no. 3, pp. 231-241, 2009. · Zbl 1273.47059
[28] W. F. Yang, “Volterra composition operators from F(p, q, s) spaces to Bloch-type spaces,” Bulletin of the Malaysian Mathematical Sciences Society, vol. 34, no. 2, pp. 267-277, 2011. · Zbl 1213.47035
[29] S. Stević, “On a new operator from H\infty to the Bloch-type space on the unit ball,” Utilitas Mathematica, vol. 77, pp. 257-263, 2008. · Zbl 1175.47034
[30] S. Stević, “On a new integral-type operator from the weighted Bergman space to the Bloch-type space on the unit ball,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 154263, 14 pages, 2008. · Zbl 1155.32002
[31] D. D. Clahane and S. Stević, “Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball,” Journal of Inequalities and Applications, vol. 2006, Article ID 61018, 11 pages, 2006. · Zbl 1131.47018
[32] J. H. Shi, “Inequalities for the integral means of holomorphic functions and their derivatives in the unit ball of \Bbb Cn,” Transactions of the American Mathematical Society, vol. 328, no. 2, pp. 619-637, 1991. · Zbl 0761.32001
[33] S. Ohno, K. Stroethoff, and R. Zhao, “Weighted composition operators between Bloch-type spaces,” The Rocky Mountain Journal of Mathematics, vol. 33, no. 1, pp. 191-215, 2003. · Zbl 1042.47018
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.