Abstract
We study the Möbius invariant spacesQ p andQ p, 0 of analytic functions. These scales of spaces include BMOA=Q 1, VMOA=Q 1, 0 and the Dirichlet space=Q 0. Using the Bergman metric, we establish decomposition theorems for these spaces. We obtain also a fractional derivative characterization for bothQ p andQ p, 0 .
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[A]Aulaskari, R., OnQ p functions, inComplex Analysis and Related Topics (Cuernavaca, 1996) (Ramírez de Arellano, E., Shapiro, M. V., Tovar, L. M. and Vasilevskiî, N. L., eds.), Oper. Theory Adv. Appl.114, pp. 21–29, Birkhäuser, Basel, 2000.
[AL]Aulaskari, R. andLappan, P., Criteria for analytic functions to be Bloch and a harmonic or meromorphic function to be normal, inComplex Analysis and its Applications (Hong Kong, 1993) (Yang, C.-C., Wen, G. C., Li, K. Y. and Chiang, Y.-M., eds.), Pitman Res. Notes Math. Ser.305, pp. 136–146, Longman Sci. Tech., Harlow, 1994.
[ANZ]Aulaskari, R., Nowak, M. andZhao, R., Thenth derivative characterization of Möbius invariant Dirichlet space,Bull. Austral. Math. Soc. 58 (1998), 43–56.
[ASX]Aulaskari, R., Stegenga, D. A. andXiao, J., Some subclasses of BMOA and their characterization in terms of Carleson measure,Rocky Mountain J. Math. 26 (1996), 485–506.
[AXZ]Aulaskari, R., Xiao, J. andZhao, R., On subspaces and subsets of BMOA and UBC,Analysis 15 (1995), 101–121.
[CR]Coifman, R. R. andRochberg, R., Representation theorems for holomorphic and harmonic functions inL P, inRepresentation Theorems for Hardy Spaces, Astérisque77, pp. 11–66, Soc. Math. France, Paris, 1980.
[EJPX]Essén, M., Janson, S., Peng, L. andXiao, J., Q spaces of several real variables,Indiana Univ. Math. J. 49 (2000), 575–615.
[G]Garnett, J. B.,Bounded Analytic Functions, Academic Press, Orlando, Fla., 1981.
[L]Lappan, P., A survey ofQ p spaces, inComplex Analysis and Related Topics (Cuernavaca, 1996) (Ramírez de Arellano, E., Shapiro, M. V., Tovar, L. M. and Vasilevskiî, N. L., eds.), Oper. Theory Adv. Appl.114, pp. 147–154, Birkhäuser, Basel, 2000.
[NX]Nicolau, A. andXiao, J., Bounded functions in Möbius invariant Dirichlet spaces,J. Funct. Anal. 150 (1997), 383–425.
[P]Power, S. C.,Hankel Operators on Hilbert Space, Pitman Res. Notes Math. Ser.64, Pitman, Boston, Mass., 1982.
[Rä]Rättyä, J., On some complex function spaces and classes,Ann. Acad. Sci. Fenn. Math. Dissertationes 124 (2001).
[R]Rochberg, R., Decomposition theorems for Bergman spaces and their applications, inOperators and Function Theory (Lancaster, 1984) (Power, S. C., ed.), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.153, pp. 225–277, Reidel, Dordrecht, 1985.
[RS]Rochberg, R. andSemmes, S., A decomposition theorem for BMO and applications,J. Funct. Anal. 67 (1986), 228–263.
[RW]Rochberg, R. andWu, Z., A new characterization of Dirichlet type spaces and applications,Illinois J. Math. 37 (1993), 101–122.
[X]Xiao, J.,Holomorphic Q Classes, Lecture Notes in Math.1767, Springer-Verlag, Berlin-Heidelberg, 2001.
[Zh]Zhao, R., On a general family of function spaces,Ann. Acad. Sci. Fenn. Math. Dissertationes 105 (1996).
[Z]Zhu, K.,Operator Theory in Function Spaces, Marcel Dekker, New York, 1990.
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Wu, Z., Xie, C. Decomposition theorems forQ p spaces. Ark. Mat. 40, 383–401 (2002). https://doi.org/10.1007/BF02384542
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DOI: https://doi.org/10.1007/BF02384542