: 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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Real interpolation between L p spaces gives [13] the family of Lorentz spaces.

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

Lions and Peetre have proved that:. 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 spaaces NLA website. If the scalars are complex numbersproperties of complex analytic functions are used to define an interpolation space.

Request this item to view in the Library’s reading rooms using your library card. Collection delivery service resumes on Wednesday 2 January From Wikipedia, the free encyclopedia. Bsrgh the order of the two spaces results in: It depends in an essential way from the specific relative position that X 0 and X 1 occupy in a larger space Z.

Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen ; In the Library Request this item to view in the Library’s reading rooms using your library card.


Equipped with these norms, the intersection and lofstrlm sum are Banach spaces. For the rest of the section, the following setting and notation will be used:.

Interpolation space

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. Functional Analysis The following inclusions are all continuous:. Interpolation studies the family of spaces X spaecs are intermediate spaces between X 0 and X 1 in the sense that. Other such questions are compactness or weak-compactness of linear operators. Several interpolation results are available for Sobolev spaces and Besov spaces on R n[26].

Interpolation does not depend only upon the isomorphic nor isometric equivalence classes of X 0 and X 1. By using this site, you agree to the Terms of Use and Privacy Policy.

Interpolation Spaces: An Introduction – Jöran Bergh, Jörgen Löfström – Google Books

Cite this Email this Add to favourites Print this page. This fact is closely related to the Riesz—Thorin theorem. National Library of Australia. Can I view this online? Details Collect From There are two ways for itnerpolation the real interpolation method. You must be logged in to Tag Records. Can I borrow this item? 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.


Further information on the Library’s opening hours is available at: In the field of mathematical analysisan interpolation space is a space which lies “in between” two other Banach spaces. 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 Interpolatin into Z is continuous.

The first and most commonly used when actually identifying examples of interpolation spaces is the K-method.

The discrete definition makes several questions easier to study, among which the already mentioned identification of the spaxes. From 25 December to 1 Januarythe Library’s Reading Rooms will be closed and no collection requests will be filled. This abstract method can be used, for example, for the proof of the following result:. The family of L p spaces consisting of complex valued functions behaves well under complex interpolation.

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