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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 2024
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:	taught
Language:	Czech, English
Teaching methods:	full-time

Guarantor:	RNDr. Daniel Cameron Campbell, Ph.D.
Teacher(s):	RNDr. Daniel Cameron Campbell, Ph.D.
Class:	M Mgr. MA M Mgr. MA > Volitelné
Classification:	Mathematics > Real and Complex Analysis

Annotation -

Hardy spaces, BMO spaces, pointwise and distributional Jacobians of Sobolev functions.

Last update: T_KMA (02.05.2013)

Course completion requirements -

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

material delivered during the lectures.

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

Literature - Czech

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.

Last update: T_KMA (02.05.2013)

Syllabus -

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

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

Entry requirements -

Measure theory, Lebesgue integration, Sobolevov spaces, singular integrals

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