: 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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To learn more about Copies Direct watch this short online video. From Wikipedia, the free encyclopedia. We will contact you if necessary. Can I borrow this item? Let X 0X 1 be a compatible couple of Banach spaces. By using this site, you agree to the Terms of Use and Privacy Policy. The discrete definition makes several questions easier to study, among which the already mentioned identification of the dual.

Cite this Email this Add to favourites Print this page. This abstract method can be used, for example, for the proof of the following result:. Changing the order of the two spaces results in: From 25 December to 1 Januarythe Library’s Reading Rooms will be closed and no collection requests will be filled.

### Interpolation spaces: an introduction – Jöran Bergh, Jörgen Löfström – Google Books

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. In simple terms, if a linear function is continuous on a certain space L p and also on a certain space L qthen it is also continuous on the space L rfor any intermediate r between p and q.

CS1 French-language sources fr. Order a copy Copyright or permission restrictions may apply.

There are two ways for introducing the real interpolation method. If the scalars are complex numbersproperties of complex analytic functions are used to define an interpolation space. You must be logged in to Tag Records. Paris in French BookOnline – Google Books.

Members of Aboriginal, Torres Strait Islander and Maori communities are advised that this catalogue contains names and images of deceased people. How do I find a book? In the field of mathematical analysisan interpolation space is a space which lies “in between” two other Banach loofstrom. This is because the K-functional K ft ; X 0X 1 of this couple is equivalent to. Retrieved from ” https: Views Read Edit View history.

Request this item to view in the Library’s reading rooms integpolation your library card. That the J- and K-methods agree is important for the study of duals of interpolation interoolation To learn more about how to request items watch this short online video.

In the development of Sobolev spaces, it became clear that the trace spaces were berh 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.

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This page was last edited on 28 Marchat The family of L p spaces consisting of complex valued functions behaves well under complex interpolation. Real interpolation between L p spaces gives [13] the family of Lorentz spaces.

Interpolation studies the family of spaces X that are intermediate spaces between X 0 and X 1 in the sense that.

A compatible couple X 0X 1 of Banach spaces consists of two Banach spaces X 0 and X 1 that are continuously embedded in the same Hausdorff topological vector space Z. Advanced search Search history. Several interpolation results are available for Sobolev spaces and Besov spaces on R n[26]. This follows from an inequality of Hardy and from the value given above of the K-functional for this compatible couple.

You can view this on the NLA website. 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.

The theorem covers degenerate cases that have not been excluded: However, there is a general relationship. Functional Analysis Other such questions are compactness or weak-compactness of linear operators.

Many methods were designed to generate such spaces of functions, including the Fourier transformcomplex interpolation, [1] real interpolation, [2] as well as other tools see e. Can I get a copy? Lions and Interoolation have proved that:.