Syllabus
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)
Annotation
Basic course on interpolation of linear and sublinear operators on function spaces. Recommended for master students of mathematical analysis.