Blaschke products, (alpha)-curves and Qp spaces

• Autorzy: Majchrowska G. , Mouratides C.
• Języki publikacji: EN

Abstrakty

EN

We give necessary and sufficient conditions for Blaschke products with zeros on an a-curve, to belong to a Qp space, in terms only of distribution of the zeros. It comes out that the condition depends on p. As we see the 0-1 law of the non tangential case breaks. Here it is possible that a Blaschke product B belongs to Qp for some but not for all p.

Słowa kluczowe

EN

Blaschke product; Qp-space

PL

iloczyn Blaschke; krzywe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2010
• Tom: Vol. 43, nr 1
• Strony: 29--38
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Majchrowska G.

autor

Mouratides C.

• Aristotle University of Thessaloniki Computer Science Department 54124 Thessaloniki, Greece,

Bibliografia

• [1] R. Aulaskari, Y. He J. Ristoja, R. Zhao, Qp spaces on Riemann surfaces, Canad. J. Math. 50 (1998), 449-464.
• [2] R. Aulaskari, D. Stegenga, J. Xiao, Some subclasses of BMOA and their characterisation in terms of carleson measures, Rocky Mountain J. Math. 26 (1996), 485-506.
• [3] R. Aulaskari, J. Xiao, R. Zhao, On subspaces and subsets of BMOA and UBC, Analysis 15 (1995), 101-121.
• [4] P. Colwell, Blaschke Products (Bounded Analytic Functions), The University of Michigan, 1985.
• [5] N. Danikas, C. Mouratides, Blaschke products in Qp spaces, Complex Variables 43 (2000), 109-209.
• [6] P. Duren, Theory of Hp spaces, Vol. 38 of Pure Appl. Math., 1970.
• [7] M. Essén, J. Xiao, Some results on Qp spaces, 0 < p < 1, J. Reine Angew. Math. 485 (1997), 173-195.
• [8] M. Essén, J. Xiao, Qp spaces - a survey, U.U.D.M. Report, 4, 1998.
• [9] J. Shapiro, Composition Operators and Classical Functions Theory, Springer Verlag, 1993.
• [10] J. Xiao, Holomorphic Q Classes, Springer Verlag, 2002