# MAI0116

Theory of Real Interpolation, an Introduction)/

Reell interpolationsteori, introduktion

**Number of credits:** 8 hp

**Examiner:** Irina Asekritova and Natan Kruglyak

**Course literature:** 1) J. Bergh, J. Löfström, Interpolation Spaces. Introduction, Berlin, Springer, 1976.

2) C. Bennet, R. Sharpley, Interpolation of Operators, Academic Press, series: Pure and applied mathematics v. 129, 1988.

**Course contents:** Some fundamental results in functional analysis: duality and reflexivity (Hahn-Banach theorem, James theorem). Rearrangement-invariant Banach function spaces (decreasing rearrangement and its properties, fundamental function, maximal function).

Banach couples, interpolation spaces, Riesz-Thorin interpolation theorem, K-,L-, E-functionals (properties and connections), real interpolation spaces constructed by K-,L-, E-functionals, equivalence theorem, reiteration theorem. Theorem on K-divisibility and general reiteration theorem. Power theorem, duality theorem. Marcinkiewicz theorem and interpolation in the scale of rearrangement-invariant Banach function spaces (Lorentz spaces).

**Organisation:** Lectures and seminars.

**Examination:** Oral presentation of assignments given during the course.

**Prerequisites:** A standard course on functional analysis.

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Last updated: 2015-09-07