Mobius invariant Besov spaces on the unit ball of \(\mathbb{C}^n\)

Małgorzata Michalska, Maria Nowak, Paweł Sobolewski

Abstract


We give new characterizations of the analytic Besov spaces \(B_p\) on the unit ball \(\mathbb{B}\) of \(\mathbb{C}^n\) in terms of oscillations and integral means over some Euclidian balls contained in \(\mathbb{B}\).

Keywords


Besov spaces; conformal Mobius transformation

Full Text:

PDF

References


Alfors, L., Mobius Transformations in Several Dimensions, Ordway Professorship Lectures in Mathematics. University of Minnesota, School of Mathematics, Minneapolis, Minn., 1981.

Duren, P., Weir, R., The pseudohyperbolic metric and Bergman spaces in the ball, Trans. Amer. Math. Soc. 359 (2007), 63-76.

Hahn, K. T., Youssfi, E. H., Mobius invariant Besov p-spaces and Hankel operators in the Bergman space on the unit ball of (mathbb{C}^n), Complex Variables Theory Appl. 17 (1991), 89-104.

Li, S., Wulan, H., Besov space on the unit ball of (mathbb{C}^n), Indian J. Math. 48 (2006), no. 2, 177-186.

Li, S., Wulan, H., Zhao, R. and Zhu, K., A characterization of Bergman spaces on the unit ball of (mathbb{C}^n), Glasgow Math. J. 51 (2009), 315-330.

Holland, F., Walsh, D., Criteria for membership of Bloch space and its subspace BMOA, Math. Ann. 273 (1986), no. 2, 317-335.

Li, S., Wulan, H. and Zhu, K., A characterization of Bergman spaces on the unit ball of (mathbb{C}^n), II, Canadian Math. Bull., to appear.

Nowak, M., Bloch space and Mobius invariant Besov spaces on the unit ball of (mathbb{C}^n), Complex Variables Theory Appl. 44 (2001), 1-12.

Ouyang, C., Yang, W. and Zhao, R., Mobius invariant (Q_p) spaces associated with the Green’s function on the unit ball of (mathbb{C}^n), Pacific J. Math. 182 (1998), no. 1, 69-99.

Pavlovic, M., A formula for the Bloch norm of a (C^1)-function on the unit ball of (mathbb{C}^n),

Czechoslovak Math. J. 58(133) (2008), no. 4, 1039-1043.

Pavlovic, M., On the Holland-Walsh characterization of Bloch functions, Proc. Edinb. Math. Soc. 51 (2008), 439-441.

Ren, G., Tu, C., Bloch space in the unit ball of (mathbb{C}^n), Proc. Amer. Math. Soc. 133 (2004), no. 3, 719-726.

Rudin, W., Function Theory in the Unit Ball of (mathbb{C}^n), Springer-Verlag, New York, 1980.

Stroethoff, K., The Bloch space and Besov space of analytic functions, Bull. Austral. Math. Soc. 54 (1996), 211-219.

Ullrich, D., Radial limits of M-subharmonic functions, Trans. Amer. Math. Soc. 292 (1985), no. 2, 501-518.

Zhu, K., Spaces of Holomorphic Functions in the Unit Ball, Springer-Verlag, New York, 2005.




DOI: http://dx.doi.org/10.2478/v10062-011-0016-3
Date of publication: 2016-07-27 21:54:10
Date of submission: 2016-07-26 21:41:01


Statistics


Total abstract view - 755
Downloads (from 2020-06-17) - PDF - 288

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2011 Małgorzata Michalska, Maria Nowak, Paweł Sobolewski