A Lueckingtype subspace of and its dual
Authors:
Pratibha Ghatage and Shun Hua Sun
Journal:
Proc. Amer. Math. Soc. 110 (1990), 767774
MSC:
Primary 46E15; Secondary 46B20
MathSciNet review:
1025278
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Abstract: The purpose of this investigation is to determine the extent to which Luecking's decomposition of Bergman spaces [4] can be extended to . The set of functions for which an atomic decomposition (using the reproducing kernel of the Bergman space) is possible turns out to be only a small part of . In this note we equip each of such functions with a new norm and study the resulting Banach space. We describe its dual and predual.
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 S. Axler, Bergman spaces and their operators, in Surveys of Some Recent Results in Operator Theory, vol. 1 (J. B. Conway and B. B. Morrel, eds.), Pitman Research Notes in Math., vol. 171, 1988, pp. 150. MR 958569 (90b:47048)
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 , Representation and duality in weighted spaces of analytic functions, Indiana University Math. J. 34 (1985), 319336. MR 783918 (86e:46020)
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 R. Rochberg, Decomposition theorems for Bergman spaces and their applications, in Operators and Function Theory (S. C. Power, ed.), D. Reidel, Dordrecht, 1985, pp. 225277. MR 810448 (87c:46032)
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 D. Sarason, Blaschke products in , Linear and Complex Analysis Problem Book (V. P. Havin, S. V. Hrusčëv, and N. K. Nickolśkii, eds.), Lecture Notes in Math., vol. 1043, Springer, Berlin, 1984, pp. 337338.
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 E. M. Stein, Singular integrals and differentiability properties of functions, Princeton University Press, Princeton, NJ, 1970. MR 0290095 (44:7280)
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 A. Shields and D. Williams, Bounded projections, duality, and multipliers in spaces of harmonic functions, J. Reine Angew. Math. 299/300 (1978), 256279. MR 0487415 (58:7053)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199010252789
PII:
S 00029939(1990)10252789
Article copyright:
© Copyright 1990 American Mathematical Society
