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Basic course on interpolation of linear and sublinear operators on function spaces. Recommended for master
students of mathematical analysis.
Last update: T_KMA (02.05.2013)
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Oral exam on a-priori known parts of the course. Last update: Pick Luboš, prof. RNDr., CSc., DSc. (09.01.2023)
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C. Bennett, R. Sharpley: Interpolation of Operators, Academic Press, Princeton, 1988.
J. Bergh, J. Löfström: Interpolation Spaces, Springer, Berlin, 1976.
L. Pick, A. Kufner, O. John and S. Fučík: Function Spaces I, De Gruyter, Berlin, 2012. Last update: Pick Luboš, prof. RNDr., CSc., DSc. (22.07.2018)
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1. Introduction
Interpolation of Lebesgue spaces, examples of operators
2. Classical interpolation theorems
Riesz theorem for positive operators, Riesz-Thorin theorem, Hausdorff-Young theorem, convolution, Riesz potential, interpolation of weak estimates, Vitali theorem, weak type (1,1) of the Hardy-Littlewood maximal operator, non-increasing rearrangement, Hardy's lemma, Lorentz spaces, Hardy-Littlewood inequality, Marcinkiewicz theorem, interpolation of compact operators, Yano's extrapolation theorem, exponential-type extrapolation
3. Real interpolation
compatible couples, sums and intersections of spaces, K-functional, interpolation pairs, interpolation spaces, basic theorem of real interpolation, K-funkcionál of (L^1,L^\infty)
Last update: Pick Luboš, prof. RNDr., CSc., DSc. (09.01.2023)
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Basic knowledge in measure theory. Last update: Pick Luboš, prof. RNDr., CSc., DSc. (09.01.2023)
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