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

DOI:
https://doi.org/10.1090/S0002-9947-1988-0951623-1

MathSciNet review:
951623

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-1988-0951623-1

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