Volterra composition operators from generally weighted Bloch spaces to Bloch-type spaces on the unit ball
Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 6, p. 412-417.

Voir la notice de l'article provenant de la source International Scientific Research Publications

Let $\varphi$ be a holomorphic self-map of the open unit ball $ \mathbb{B}, g \in H(\mathbb{B})$. In this paper, the boundedness and compactness of the Volterra composition operator $T^\varphi_g$ from generally weighted Bloch spaces to Bloch-type spaces are investigated.
DOI : 10.22436/jnsa.005.06.01
Classification : 47B38
Keywords: Volterra composition operator, generally weighted Bloch space, boundedness, compactness.

Li, Haiying 1 ; Zhang, Haixia 1

1 College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, P. R. China
@article{JNSA_2012_5_6_a0,
     author = {Li, Haiying and Zhang, Haixia},
     title = {Volterra composition operators from generally weighted {Bloch} spaces to {Bloch-type} spaces on the unit ball},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {412-417},
     publisher = {mathdoc},
     volume = {5},
     number = {6},
     year = {2012},
     doi = {10.22436/jnsa.005.06.01},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.06.01/}
}
TY  - JOUR
AU  - Li, Haiying
AU  - Zhang, Haixia
TI  - Volterra composition operators from generally weighted Bloch spaces to Bloch-type spaces on the unit ball
JO  - Journal of nonlinear sciences and its applications
PY  - 2012
SP  - 412
EP  - 417
VL  - 5
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.06.01/
DO  - 10.22436/jnsa.005.06.01
LA  - en
ID  - JNSA_2012_5_6_a0
ER  - 
%0 Journal Article
%A Li, Haiying
%A Zhang, Haixia
%T Volterra composition operators from generally weighted Bloch spaces to Bloch-type spaces on the unit ball
%J Journal of nonlinear sciences and its applications
%D 2012
%P 412-417
%V 5
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.06.01/
%R 10.22436/jnsa.005.06.01
%G en
%F JNSA_2012_5_6_a0
Li, Haiying; Zhang, Haixia. Volterra composition operators from generally weighted Bloch spaces to Bloch-type spaces on the unit ball. Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 6, p. 412-417. doi : 10.22436/jnsa.005.06.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.06.01/

[1] Brown, L.; Shields, A. L. Multipliers and cyclic vectors in the Bloch space, Michigan Math. J. , Volume 38 (1991), pp. 141-146

[2] Cowen, C. C.; B. D. MacCluer Composition operators on spaces of analytic functions, CRC Press, Boca Roton, 1995

[3] Li, H.; Liu, P. Weighted compositioin operators between \(H^\infty\) and generally weighted Bloch spaces of polydisk, International Journal of Mathematics, Volume 21(5) (2010), pp. 687-699

[4] Li, H.; Liu, P. Composition operators between generally weighted Bloch space and \(Q^q_{\log}\) space, Banach Journal of Mathematical Analysis, Volume 3(1) (2009), pp. 99-110

[5] Li, H.; Yang, X. Products of integral-type and composition operators from generally weighted Bloch space to F(p; q; s) space, Filomat, Volume 23(3) (2009), pp. 231-241

[6] Li, S. Volterra composition operators between weighted Bergman spaces and Bloch type spaces , J. Korean Math. Soc., Volume 45(1) (2008), pp. 229-248

[7] Shapiro, J. H. Composition operators and classical function theory, Springer-Verlag, New York, 1993

[8] Shields, A. L.; Williams, D. L. Bounded proje ctions,duality, and multipliers in spaces of analytic functions, Trans. Amer. Math. Soc., Volume 162 (1971), pp. 287-302

[9] S. Stević Norm of weighted composition operators from Bloch space to \(H_\mu^\infty\) on the unit ball , Ars. Combin, Volume 88 (2008), pp. 125-127

[10] X. Tang Extended Cesàro operators between Bloch-type spaces in the unit ball of \(\mathbb{C}^n\), J. Math. Anal. Appl. , Volume 326(2) (2007), pp. 1199-1211

[11] Xiao, J. Riemann-Stieltjes operators between weighted Bloch and Bergman spaces of the unit ball, J. London. Math. Soc. , Volume 70(2) (2004), pp. 199-214

[12] Ye, S. Weighted composition operators between different weighted Bloch-type spaces, Acta Mathematica Sinica, Chinese Series, Volume 50(4) (2007), pp. 927-942

[13] Yoneda, R. The composition operator on weighted Bloch space, Arch. Math., Volume 78 (2002), pp. 310-317

[14] Zhu, K. Spaces of Holomorphic functions in the unit ball, Springer, New York, 2005

[15] Zhu, X. Volterra composition operators on logarithmic Bloch spaces , Banach J. Math. Anal. , Volume 3(1) (2009), pp. 122-130

Cité par Sources :