: Interpolation Spaces (Grundlehren der mathematischen Wissenschaften) (): J. Bergh, J. Lofstrom: Books. Citation. Bennett, Colin. Review: Jöran Bergh and Jörgen Löfström, Interpolation spaces, an introduction. Bull. Amer. Math. Soc. 84 (), no. 1, Interpolation spaces: an introduction. Front Cover. Jöran Bergh, Jörgen Löfström. Springer, – Mathematics – pages.
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The family of L p spaces consisting of complex valued functions behaves well under complex interpolation. The main applications are in Sobolev spaceswhere spaces of functions that have a noninteger number of derivatives are interpolated from the spaces of functions with integer number of derivatives.
Several interpolation results are available for Sobolev spaces and Besov spaces on R n. The discrete definition makes several questions easier to study, among which the already mentioned identification of the dual. Functional Analysis This page was last edited on 28 Marchat The first and most commonly used when actually identifying examples of interpolation spaces is the K-method.
A Banach space X is said to be continuously embedded in a Hausdorff topological vector space Z when X is a linear subspace of Z such that the inclusion map from X into Z is continuous.
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Let X 0X 1 be a compatible couple of Banach spaces. From Wikipedia, the free encyclopedia. BookOnline – Google Books. To learn more about Copies Direct watch this short online video. Can I get a copy? Browse titles authors subjects uniform titles series callnumbers dewey numbers starting from optional.
You can view this on the NLA website. Other such questions are compactness or weak-compactness of linear operators. The K-method of real interpolation  can be used for Banach spaces over the field R of real numbers. The following inclusions are all continuous:. In the special case where X 0 is continuously embedded in X 1one can omit the part of the series with negative indices n.
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This abstract method can be used, for example, for the proof of the following result:. This is because the K-functional K ft ; X 0X 1 of this couple is equivalent to. In the development of Sobolev spaces, it became clear that the trace spaces were not any of the usual function spaces with integer number of derivativesand Jacques-Louis Lions discovered that indeed these trace spaces were constituted of functions that have a noninteger degree of differentiability.
In other words, L r is a space which is begrh between L p and L q. In the field of mathematical analysisbetgh interpolation space is a space which lies “in between” vergh other Banach spaces.
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Bennett : Review: Jöran Bergh and Jörgen Löfström, Interpolation spaces, an introduction
Many methods were designed to generate such spaces of functions, including the Fourier transformcomplex interpolation,  real interpolation,  as well as other tools see e. We will contact you if necessary. This fact is closely related to the Riesz—Thorin theorem. You must be logged in to Tag Records.
In the Library Request this item to view in the Library’s reading rooms using your library card. Changing the order of the two spaces results in: Equipped with interpolatioj norms, the intersection and the sum are Banach spaces.
New search User lists Site feedback Ask a librarian Help. Catalogue Persistent Identifier https: Details Collect From For the rest of the section, the following setting and notation will be used:. See what’s been added lkfstrom the collection in the current 1 2 3 4 5 6 weeks months years. Views Read Edit View history. This follows from an inequality of Hardy and from the value given above of the K-functional for this compatible couple.
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