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Volterra-type operators on Zygmund spaces. (English) Zbl 1146.30303
In this paper the authors study the boundedness and compactness of integral operators on the Zygmund space and the little Zygmund space.

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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[1] Duren PL: Theory of H\^{}{\(p\)}Spaces, Pure and Applied Mathematics.Volume 38. Academic Press, New York, NY, USA; 1970:xii+258.
[2] Pommerenke, Ch, Schlichte funktionen und analytische funktionen von beschränkter mittlerer oszillation, Commentarii Mathematici Helvetici, 52, 591-602, (1977) · Zbl 0369.30012
[3] Aleman, A; Siskakis, AG, An integral operator on[inlineequation not available: see fulltext.], Complex Variables. Theory and Application, 28, 149-158, (1995) · Zbl 0837.30024
[4] Aleman, A; Siskakis, AG, Integration operators on Bergman spaces, Indiana University Mathematics Journal, 46, 337-356, (1997) · Zbl 0951.47039
[5] Aleman, A; Cima, JA, An integral operator on[inlineequation not available: see fulltext.] and Hardy’s inequality, Journal d’Analyse Mathématique, 85, 157-176, (2001) · Zbl 1061.30025
[6] Benke, G; Chang, D-C, A note on weighted Bergman spaces and the Cesàro operator, Nagoya Mathematical Journal, 159, 25-43, (2000) · Zbl 0981.32001
[7] Chang, D-C; Gilbert, R; Tie, J, Bergman projection and weighted holomorphic functions, No. 143, 147-169, (2003), Basel, Switzerland · Zbl 1049.32007
[8] Chang, D-C; Stević, S, The generalized Cesàro operator on the unit polydisk, Taiwanese Journal of Mathematics, 7, 293-308, (2003) · Zbl 1065.47033
[9] Hu, Z, Extended Cesàro operators on mixed norm spaces, Proceedings of the American Mathematical Society, 131, 2171-2179, (2003) · Zbl 1054.47023
[10] Hu, Z, Extended Cesáro operators on the Bloch space in the unit ball of[inlineequation not available: see fulltext.], Acta Mathematica Scientia. Series B. English Edition, 23, 561-566, (2003) · Zbl 1044.47023
[11] Li, S, Riemann-Stieltjes operators from[inlineequation not available: see fulltext.] spaces to[inlineequation not available: see fulltext.]-Bloch spaces on the unit ball, Journal of Inequalities and Applications, 2006, 14 pages, (2006) · Zbl 1131.47030
[12] Li, S; Stević, S, Reimann-stieltjies type integral operators on the unit ball in[inlineequation not available: see fulltext.], No. 2, (2007)
[13] Siskakis, AG; Zhao, R, A Volterra type operator on spaces of analytic functions, No. 232, 299-311, (1999), Providence, RI, USA · Zbl 0955.47029
[14] Stević, S, Cesàro averaging operators, Mathematische Nachrichten, 248/249, 185-189, (2003) · Zbl 1024.47014
[15] Stević, S, On an integral operator on the unit ball in[inlineequation not available: see fulltext.], Journal of Inequalities and Applications, 2005, 81-88, (2005) · Zbl 1074.47013
[16] Stević, S, Boundedness and compactness of an integral operator on a weighted space on the polydisc, Indian Journal of Pure and Applied Mathematics, 37, 343-355, (2006) · Zbl 1121.47032
[17] Tamrazov, PM, Contour and solid structure properties of holomorphic functions of a complex variable, Russian Mathematical Surveys, 28, 141-1731, (1973) · Zbl 0273.30036
[18] Cowen CC, MacCluer BD: Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics. CRC Press, Boca Raton, Fla, USA; 1995:xii+388.
[19] Madigan, K; Matheson, A, Compact composition operators on the Bloch space, Transactions of the American Mathematical Society, 347, 2679-2687, (1995) · Zbl 0826.47023
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