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Course, academic year 2023/2024
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Advanced Differentiation and Integration 4 - NMMA564
Title: Derivace a integrál pro pokročilé 4
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: summer
E-Credits: 3
Hours per week, examination: summer 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
Guarantor: RNDr. Daniel Cameron Campbell, Ph.D.
Class: M Mgr. MA
M Mgr. MA > Volitelné
Classification: Mathematics > Real and Complex Analysis
Annotation -
Last update: T_KMA (02.05.2013)
Hardy spaces, BMO spaces, pointwise and distributional Jacobians of Sobolev functions.
Course completion requirements -
Last update: prof. RNDr. Jan Malý, DrSc. (10.05.2018)

The course is completed by an oral exam. The required knowledge corresponds to the

material delivered during the lectures.

Literature - Czech
Last update: T_KMA (02.05.2013)

E. M. Stein: Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. Princeton University Press, Princeton, NJ, 1993.

T. Iwaniec, G. Martin: Geometric function theory and non-linear analysis. The Clarendon Press, Oxford University Press, New York, 2001.

Syllabus -
Last update: prof. RNDr. Jan Malý, DrSc. (10.05.2018)

Hardy spaces

atomic decomposition

real-analytic definitions

boundedness of singular integrals on H^1

BMO space

VMO space

Fefferman-Stein inequality

duality VMO-H^1-BMO

distributional Jacobian

Hardy-1 estimates of Jacobian of a W^{1,n}-function

Entry requirements -
Last update: prof. RNDr. Jan Malý, DrSc. (10.05.2018)

Measure theory, Lebesgue integration, Sobolevov spaces, singular integrals

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