Last update: doc. RNDr. Pavel Pyrih, CSc. (04.05.2018)
Prof. Carlos Perez (BCAM Bilbao, Spain) will deliver a series
of 10 lectures with the title "An Introduction to the Theory of
Weights in Harmonic Analysis". The course will take place
in the week September 26 - September 30,2016.
Last update: doc. RNDr. Pavel Pyrih, CSc. (04.05.2018)
Prof. Carlos Perez (BCAM Bilbao, Španělsko) přednese anglicky
cyklus 10 přednášek s názvem "An Introduction to the Theory of
Weights in Harmonic Analysis". Kurz se koná v týdnu 26.9.-30.9.2016.
Syllabus
Last update: doc. RNDr. Pavel Pyrih, CSc. (04.05.2018)
In this minicourse we will give a short introduction to some aspects of the Calder\'on-Zygmund theory that will lead to the study of Singular Integral Operators with weights with sharp bounds. First we will provide a revised version of some classical results: $A_p$ theorem of Muckenhoupt, good-$\lambda$ inequalities, John-Nirenberg theorem lemma for $B.M.O.$ functions, Rubio de Francia's extrapolation theorem, factorization theorem. The approach differs from the classical ones but the common ground is still the Calder\'on-Zygmund real analysis method. We will present some modern results for Singular Integrals on weighted $L^p$ spaces assuming that the weight satisfies the $A_1$ or the $A_p$ condition. If there is time we will also prove sharp endpoint results. We will show some connections with other related topics: Commutators with BMO functions, two-weight theory etc. During the lectures we will be presenting some open problems in the area.
