Interpolation of Vector Measures
Let （Ω, ∑） be a measurable space and mo ： E→ Xo and m1 ： E → X1 be positive vector measures with values in the Banach KSthe function spaces Xo and X1. If 0 〈 a 〈 1, we define a X01-ax1a new vector measure [m0, m]a with values in the Calderdn lattice interpolation space and we analyze the space of in...
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| Published in: | Acta mathematica Sinica. English series Vol. 27; no. 1; pp. 119 - 134 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Heidelberg
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
2011
Springer Nature B.V |
| Subjects: | |
| Online Access: | Get full text |
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| Summary: | Let （Ω, ∑） be a measurable space and mo ： E→ Xo and m1 ： E → X1 be positive vector measures with values in the Banach KSthe function spaces Xo and X1. If 0 〈 a 〈 1, we define a X01-ax1a new vector measure [m0, m]a with values in the Calderdn lattice interpolation space and we analyze the space of integrable functions with respect to measure [m0, m1]a in order to prove suitable extensions of the classical Stein Weiss formulas that hold for the complex interpolation of LP-spaces. Since each p-convex order continuous Kothe function space with weak order unit can be represented as a space of p-integrable functions with respect to a vector measure, we provide in this way a technique to obtain representations of the corresponding complex interpolation spaces. As applications, we provide a Riesz-Thorin theorem for spaces of p-integrable functions with respect to vector measures and a formula for representing the interpolation of the injective tensor product of such spaces. |
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| Bibliography: | O174.12 Interpolation, Banach function space, vector measure O177.3 11-2039/O1 ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 1439-8516 1439-7617 |
| DOI: | 10.1007/s10114-011-9542-8 |