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Cubo (Temuco)

versão On-line ISSN 0719-0646

Cubo vol.14 no.1 Temuco  2012

http://dx.doi.org/10.4067/S0719-06462012000100002 

CUBO A Mathematical Journal Vol.14, N° 01, (09-19). March 2012

 

Integral composition operators between weighted Bergman spaces and weighted Bloch type spaces

 

Elke Wolf

University of Paderborn, Mathematical Institute, D-33095 Paderborn, Germany, email: lichte@math.uni-paderborn.de


ABSTRACT

We characterize boundedness and compactness of integral composition operators acting between weighted Bergman spaces Av,p and weighted Bloch type spaces Bw.

 

Keywords and Phrases: Weighted Bergman spaces, integral composition operator, weighted Bloch type spaces

2010 AMS Mathematics Subject Classification: 47B33, 47B38.


RESUMEN

Caracterizamos la acotación y compacidad de operadores integrales compuestos actuando entre espacios de Bergman con peso Av,p y espacios Bw de tipo Bloch con peso.


 

References

[1] A. Aleman, J.A. Cima, An integral operator on Hp and Hardy's inequality, J. Anal. Math. 85 (2001), 157-176        [ Links ]

[2] A. Aleman, A. G. Siskakis, An integral operator on Hp, Complex Variables Theory Appl. 28 (1995), no. 2, 149- 158.         [ Links ]

[3] A. Aleman, A. G. Siskakis, Integration operators on Bergman spaces, Indiana University Math. J. 46 (1997), no. 2, 337-356.         [ Links ]

[4] J. Bonet, P. Dománski, M. Lindström, Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions, Canad. Math. Bull. 42, no. 2, (1999), 139-148.         [ Links ]

[5] J. Bonet, P. Dománnski, M. Lindström, J. Taskinen, Composition operators between weighted Banach spaces of analytic functions, J. Austral. Math. Soc. (Serie A) 64 (1998), 101-118.         [ Links ]

[6] J. Bonet, M. Friz, E. Jordá, Composition operators between weighted inductive limits of spaces of holomorphic functions, Publ. Math. 67 (2005), no. 3-4, 333-348.         [ Links ]

[7] J. Bonet, M. Lindström, E. Wolf, Differences of composition operators between weighted Banach spaces of holomorphic functions, to appear in J. Austr. Math. Soc.         [ Links ]

[8] M.D. Contreras, A.G. Hernández-Díaz, Weighted composition operators in weighted Banach spaces of analytic functions, J. Austral. Math. Soc. (Serie A) 69 (2000), 41-60.         [ Links ]

[9] C. Cowen, B. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, 1995.         [ Links ]

[10] P. Dománski, M. Lindström, Sets of interpolation and sampling for weighted Banach spaces of holomorphic functions, Ann. Pol. Math (2002) 79, 233-264.         [ Links ]

[11] P. Duren, A. Schuster, Bergman spaces, Mathematical Surveys and Monographs 100, American Mathematical Society, Providence, RI, 2004.         [ Links ]

[12] H. Hedenmalm, B. Korenblum, K. Zhu, Theory of Bergman spaces, Graduate Texts in Mathematics 199, Springer-Verlag, New York, 2000.         [ Links ]

[13] S. Li, Volterra composition operators between weighted Bergman spaces and Bloch type spaces, J. Korean Math. Soc. 45(2008), no. 1, 229-248.         [ Links ]

[14] M. Lindström, E. Wolf, Essential norm of the difference of weighted composition operators, Monatsh. Math (2008) 153, 133-143.         [ Links ]

[15] W. Lusky, On the structure of Hv0(D) and hv0(D), Math. Nachr. 159 (1992), 279-289.         [ Links ]

[16] J.H. Shapiro, Composition Operators and Classical Function Theory, Springer, 1993.         [ Links ]

[17] A. G. Sisakis, R. Zhao, A Volterra type oprator on spaces of analytic functions, Functions spaces (Edwardville IL, 1998), 299-311, Contemp. Math. 232, Amer. Math. Soc. Providence, RI, 1999.         [ Links ]

[18] E. Wolf, Weighted composition operators between weighted Bergman spaces, RACSAM Rev. R. Acad. Cien. Serie A Mat. 103, no. 1, 11-15.         [ Links ]

[19] E. Wolf, Volterra composition operators between weighted Bergman spaces and weighted Bloch type spaces, Collect Math. 61 (2010), no. 1, 57-63.         [ Links ]

[20] E. Wolf, Differences of weighted compostiion operators between Bergman spaces and weighted Banach spaces of holomorphic functions, Glasgow Math. J. 52 (2010), 325-332.         [ Links ]

[21] J. Xiao, Riemann-Stieltjes operators on weighted Bloch and Bergman spaces of the unit ball, J. London, Math. Soc. (2), 70 (2004), no. 1, 199-214        [ Links ]

Received: March 2011. Revised: April 2011.