Volterra operators and semigroups in weighted Banach spaces of analytic functions

Collectanea Mathematica - Tập 65 Số 2 - Trang 233-249 - 2014
Manuela Basallote1, Manuel D. Contreras1, Carmen Hernández-Mancera1, María J. Martín2, Pedro J. Paúl1
1Departamento de Matemática Aplicada II, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092,  Seville, Spain
2Departamento de Matemáticas (Módulo 17, Edificio de Ciencias), Universidad Autónoma de Madrid, 28049 Madrid, Spain

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Tài liệu tham khảo

Abakumov, E., Doubtsiv, E.: Reverse estimates in growth spaces, to appear in Math. Z. 271, 399–413 (2012)

Abate, M.: Iteration Theory of Holomorphic Maps on Taut Manifolds. Mediterranean Press, Rende (1989)

Aleman, A.: A class of integral operators on spaces of analytic functions. In: Topics in Complex Analysis and Operator Theory, pp. 3–30. Univ. Málaga, Málaga (2007)

Aleman, A., Cima, J.A.: An integral operator on $$H^p$$ H p and Hardy’s inequality. J. Anal. Math. 85, 157–176 (2001)

Aleman, A., Siskakis, A.G.: An integral operator on $$H^p$$ H p . Complex Var. Theory Appl. 28, 149–158 (1995)

Aleman, A., Siskakis, A.G.: Integration operators on Bergman spaces. Indiana Univ. Math. J. 46, 337–356 (1997)

Berkson, E., Porta, H.: Semigroups of analytic functions and composition operators. Mich. Math. J. 25, 101–115 (1978)

Bierstedt, K.D., Bonet, J., Taskinen, J.: Associated weights and spaces of holomorphic functions. Studia Math. 127, 137–168 (1998)

Blasco, O., Contreras, M.D., Díaz-Madrigal, S., Martínez, J., Siskakis, A.G.: Semigroups of composition operators in BMOA and the extension of a theorem of Sarason. Int. Equ. Oper. Theory 61, 45–62 (2008)

Blasco, O., Contreras, M.D., Díaz-Madrigal, S., Martínez, J., Papadimitrakis, M., Siskakis, A.G.: Semigroups of composition operators and integral operators in spaces of analytic functions. Ann. Acad. Sci. Fenn. Math. 38, 67–89 (2013)

Bonet, J., Domański, P., Lindström, M., Taskinen, J.: Composition operators between weighted Banach spaces of analytic functions. J. Aust. Math. Soc. (Ser. A) 64, 101–118 (1998)

Bourgain, J.: $$H^{\infty }$$ H ∞ is a Grothendieck space. Studia Math. 75, 193–216 (1983)

Bourgain, J.: New Banach space properties of the disc algebra and $$H^{\infty }$$ H ∞ . Acta Math. 152, 1–48 (1984)

Contreras, M.D., Díaz-Madrigal, S.: Fractional iteration in the disk algebra: prime ends and composition operators. Revista Mat. Iberoamericana 21, 911–928 (2005)

Contreras, M.D., Hernández-Díaz, A.G.: Weighted composition operators in weighted Banach spaces of analytic functions. J. Aust. Math. Soc. (Ser. A) 69, 41–60 (2000)

Danikas, N., Siskakis, A.G.: The Cesàro operator on bounded analytic functions. Analysis 13, 295–299 (1993)

Diestel, J.: Sequences and Series in Banach Spaces. Springer-Verlag, New York (1984)

Domański, P., Lindström, M.: Sets of interpolation and sampling for weighted Banach spaces of holomorphic functions. Ann. Polon. Math. 89, 233–264 (2002)

Dunford, N., Schwartz, J.T.: Linear Operators I. Interscience Publishers. Wiley, New York (1958)

Duren, P.L.: Theory of $$H^p$$ H p spaces, Academic Press, New York (1970) (Reprinted by Dover, Mineola, NY (2000))

Galanopoulos, P., Girela, D., Peláez, J.A.: Multipliers and integration operators on Dirichlet spaces. Trans. Am. Math. Soc. 363(4), 1855–1886 (2011)

Hardy, G.H., Littlewood, J.E.: Some properties of fractional integrals. II. Math. Z. 34(1), 403–439 (1932)

Harutyunyan, A., Lusky, W.: On the boundedness of the differentiation operator between weighted spaces of holomorphic functions. Studia Math. 184, 233–247 (2008)

Hu, Z.: Extended Cesàro operators on mixed-norm spaces. Proc. Am. Math. Soc. 131(7), 2171–2179 (2003)

Li, S., Stević, S.: Products of Volterra type operator and composition operator from $$H^{\infty }$$ H ∞ and Bloch spaces to Zygmund spaces. J. Math. Anal. Appl. 345, 40–52 (2008)

Lotz, H.P.: Uniform convergence of operators on $$L^{\infty }$$ L ∞ and similar spaces. Math. Z. 190, 207–220 (1985)

Lusky, W.: Growth conditions for harmonic and holomorphic functions. In: Dierolf, S. et al (eds.) Functional Analysis (Trier,1994), pp. 281–291. de Gruyter (1996)

Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Studia Math. 175, 19–45 (2006)

Pau, J., Peláez, J.A.: Embedding theorems and integration operators on Bergman spaces with rapidly decreasing weights. J. Funct. Anal. 259(10), 2727–2756 (2010)

Pommerenke, Ch.: Univalent Functions. Vandenhoeck & Ruprecht, Göttingen (1975)

Pommerenke, Ch.: Schlichte funktionen und analytische funktionen von beschränkter mittlerer oszilation. Comment. Math. Helv. 52, 591–502 (1977)

Rubel, L.A., Shields, A.L.: The second duals of certain spaces of analytic functions. J. Aust. Math. Soc. 11, 276–280 (1970)

Shields, A.L., Williams, D.L.: Bounded projections, duality, and multipliers in spaces of analytic functions. Trans. Am. Math. Soc. 162, 287–302 (1971)

Shields, A.L., Williams, D.L.: Bounded projections and the growth of harmonic conjugates in the unit disc. Mich. Math. J. 29, 3–25 (1982)

Shoikhet, D.: Semigroups in Geometrical Function Theory. Kluwer Academic Publishers, Dordrecht (2001)

Siskakis, A.G.: Semigroups of composition operators on the Dirichlet space. Result Math. 30, 165–173 (1996)

Siskakis, A.G.: Semigroups of composition operators on spaces of analytic functions, a review. In: Contemporary Mathematics, vol. 213, pp. 229–252. American Mathematical Society, Providence (1998)

Stević, S.: Extended Cesàro operators between mixed-norm spaces and Bloch-type spaces in the unit ball. Houst. J. Math. 36, 84–858 (2010)

Wirths, K.J., Xiao, J.: Recognizing $$Q_{p,0}$$ Q p , 0 functions as per Dirichlet space structure. Bull. Belg. Math. Soc. 8, 47–59 (2001)

Wolf, E.: Volterra composition operators between weighted Bergman spaces and weighted Bloch type spaces. Collect. Math. 61, 57–63 (2010)

Wolf, E.: Products of Volterra type operators and composition operators between weighted Bergman spaces of infinite order and weighted Bloch type spaces. Georgian Math. J. 17, 621–627 (2010)

Xiao, J.: Holomorphic $$Q$$ Q Classes, Lecture Notes in Mathematics, 1767. Springer-Verlag, Berlin (2001)

Yoneda, R.: Integration operators on weighted Bloch spaces. Nihonkai Math. J. 12, 123–133 (2001)

Zhu, K.: Operator Theory in Function spaces. Marcel Dekker, Inc., New York (1990)