: 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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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.

### Bennett : Review: Jöran Bergh and Jörgen Löfström, Interpolation spaces, an introduction

Retrieved from ” https: We will contact you if necessary. There are two ways for introducing the real interpolation method. The family of L p spaces consisting of complex valued functions behaves well under complex interpolation. In the field of mathematical analysisan interpolation space is a space which lies “in between” two other Banach spaces. BookOnline – Google Lofstroom. CS1 French-language sources fr.

Die Grundlehren der mathematischen Psaces in Einzeldarstellungen ; 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. To learn more about how to request items watch this short online video. How do I find beegh book? Let X 0X 1 be a compatible couple of Banach spaces. 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 lostrom the space L rfor any intermediate r between p and q.

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. You can view this on the NLA website.

Changing the order of the two spaces results in: A complex interpolation space is usually not isomorphic to one of the spaces given by the real interpolation method. It depends in an essential way from the specific relative position that X 0 and X 1 occupy in a larger space Z. 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.

## Interpolation space

Collection delivery service resumes on Wednesday lofwtrom January Interpolation does not depend only upon the isomorphic nor isometric equivalence classes of X 0 and X 1. Advanced search Search history.

Banach spaces Sobolev spaces Fourier analysis. Request this item to view in the Library’s reading rooms using your library card. Functional Analysis Several interpolation results are available for Sobolev spaces and Besov spaces on R n[26].

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

Can I view this online? Real interpolation between L p spaces gives [13] the family of Lorentz spaces. However, there is a general relationship. Can I borrow this item? In the Library Request this item to view in the Library’s reading rooms using your library card. Can I get a copy? This fact is closely related to the Riesz—Thorin theorem. Other such questions are compactness or weak-compactness of linear operators.

For the rest of the section, the following setting and notation will be used:. Order a copy Copyright or permission restrictions may apply.

See what’s been added to the collection in the current 1 2 3 4 5 6 weeks months years. Lions and Peetre have proved that:.

That the J- and K-methods agree is important for the study of duals of interpolation spaces: The theorem covers degenerate cases that have not been excluded: Further information on bergn Library’s opening hours is available at: Interpolation studies the family of spaces X that are intermediate spaces between X 0 and X 1 in the sense that. This is because the K-functional K ft ; X 0X 1 of this couple is equivalent to.

The discrete definition makes several questions easier to study, among which the already mentioned identification of the dual. In other words, Lofstron r is a space which is intermediate between L p and L q.