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ON R-SECTORIAL DERIVATIVES ON BERGMAN SPACES

Part of: Groups and semigroups of linear operators, their generalizations and applications Holomorphic functions of several complex variables

Published online by Cambridge University Press:  01 April 2008

TOMÁŠ BÁRTA
TOMÁŠ BÁRTA*
Affiliation:
Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Prague, Sokolovska 83, 180 00 Prague 8, Czech Republic (email: barta@karlin.mff.cuni.cz)
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Abstract

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In this paper we show boundedness of vector-valued Bergman projections on simple connected domains. With this result we show R-sectoriality of the derivative on the Bergman space on C+ and maximal Lp-regularity for an integrodifferential equation with a kernel in the Bergman space.

Keywords

Bergman projectionR-sectorialityintegrodifferential equationsmaximal regularity

MSC classification

Secondary: 47D06: One-parameter semigroups and linear evolution equations 32A36: Bergman spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 2 , April 2008 , pp. 305 - 313
Copyright
Copyright © 2008 Australian Mathematical Society

References

[1]Arregui, J. L. and Blasco, O., ‘Bergman and Bloch spaces of vector-valued functions’, Math. Nachr. 261 (2003), 3–22.CrossRefGoogle Scholar
[2]Bárta, T., ‘Analytic solutions of Volterra equations via semigroups’, Semigroup Forum 76(1) (2008), 142–148.CrossRefGoogle Scholar
[3]Bekollé, D. and Bonami, A., ‘Inégalités à poids pour le noyau de Bergman’, C. R. Acad. Sci. Paris Sér. A–B 286 (1978), A775–A778.Google Scholar
[4]Denk, R., Hieber, M. and Prüss, J., ‘R-boundedness, Fourier multipliers and problems of elliptic and parabolic type’, Mem. Amer. Math. Soc. 166(788) (2003).Google Scholar
[5]Dore, G., ‘Maximal regularity in L p spaces for an abstract Cauchy problem’, Adv. Differential Equations 5 (2000), 293–322.CrossRefGoogle Scholar
[6]Engel, K. J. and Nagel, R., One-parameter semigroups for linear evolution equations, Graduate Texts in Mathematics, 194 (Springer, Berlin, 2000).Google Scholar
[7]Hedenmalm, H., ‘The dual of a Bergman space on simply connected domains’, J. Anal. Math. 88 (2002), 311–335.CrossRefGoogle Scholar
[8]Kunstmann, P. and Weis, L., ‘Perturbation theorems for maximal L p-regularity’, Ann. Sc. Norm. Super. Pisa Cl. Sci. 30 (2001), 415–435.Google Scholar
[9]Nagel, R., ‘Towards a ‘matrix theory’ for unbounded operator matrices’, Math. Z. 201 (1989), 57–68.CrossRefGoogle Scholar
[10]Weis, L., ‘Operator-valued Fourier multiplier theorems and maximal L p-regularity’, Math. Ann. 319 (2001), 735–758.CrossRefGoogle Scholar
[11]Weis, L., A new approach to maximal L p-regularity, evolution equations and their applications in physical and life sciences (Bad Herrenalb, 1998), Lecture Notes in Pure and Applied Mathematics, 215 (Marcel Dekker, New York, 2001), pp. 195–214.Google Scholar