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Course, academic year 2023/2024
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Introduction to Interpolation Theory 1 - NMMA533
Title: Úvod do teorie interpolací 1
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: winter
E-Credits: 4
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Class: M Mgr. MA
M Mgr. MA > Povinně volitelné
Classification: Mathematics > Functional Analysis, Real and Complex Analysis
Incompatibility : NRFA045
Interchangeability : NRFA045
Is interchangeable with: NRFA045
Annotation -
Last update: T_KMA (02.05.2013)
Basic course on interpolation of linear and sublinear operators on function spaces. Recommended for master students of mathematical analysis.
Course completion requirements -
Last update: prof. RNDr. Luboš Pick, CSc., DSc. (09.01.2023)

Oral exam on a-priori known parts of the course.

Literature -
Last update: prof. RNDr. Luboš Pick, CSc., DSc. (22.07.2018)

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.

Syllabus -
Last update: prof. RNDr. Luboš Pick, CSc., DSc. (09.01.2023)

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)

Entry requirements -
Last update: prof. RNDr. Luboš Pick, CSc., DSc. (09.01.2023)

Basic knowledge in measure theory.

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