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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Complex interpolation of normed and quasinormed spaces in several dimensions. I


Author: Zbigniew Slodkowski
Journal: Trans. Amer. Math. Soc. 308 (1988), 685-711
MSC: Primary 32F05; Secondary 32E30, 32M10, 46M35
MathSciNet review: 951623
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Abstract: A variety of complex interpolation methods for families of normed or quasi-normed spaces, parametrized by points of domains in complex homogeneous spaces, parametrized by points of domains in complex homogeneous spaces, is developed. Results on existence, continuity, uniqueness, reiteration and duality for interpolation are proved, as well as on interpolation of operators. A minimum principle for plurisubharmonic functions is obtained and used as a tool for the duality theorem.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0951623-1
PII: S 0002-9947(1988)0951623-1
Keywords: Interpolation spaces, subinterpolation and superinterpolation families, plurisubharmonic functions, subharmonic functions, pseudoconvex classes, Dirichlet problem, complex homogeneous spaces, strictly pseudoconvex domains
Article copyright: © Copyright 1988 American Mathematical Society