RG Analysis and Partial Differential Equations
V5B8: Selected Topics in Analysis - Weighted inequalities
Summer Semester 2017
- Dr. Pavel Zorin-Kranich
- Instructor
Lectures
- Friday 10-12, SR 0.011
Exam
Oral exams take place on August 4 and August 10.Topics
The lecture notes cover the topics listed below unless there is a link to an external source.- Fefferman-Stein inequality
- The Ap condition
- Extrapolation, sparse operators
- Calderón-Zygmund operators
- Calderón-Zygmund operators, continued
- May 26: sparse domination for a nontangentional maximal operator
- June 2: A∞ and the reverse Hölder inequality
- June 23: mixed A∞ estimates
- June 30: intrinsic square function, only Section 2 without Lemma 2.2 and with v=1, beta=1.
- July 7: Embedding A∞ into Ap; Orlicz spaces
- July 14: Fefferman-Stein type inequality for sparse operators, following this article, another proof of sparse domination following this article
- July 21: Counterexample to Muckenhoupt-Wheeden conjecture
Literature
- J. Duoandikoetxea. “Extrapolation of weights revisited: new proofs and sharp bounds”. In: J. Funct. Anal. 260.6 (2011), pp. 1886–1901.
- C. Fefferman and E. M. Stein. Some Maximal Inequalities, American Journal of Mathematics Vol. 93, No. 1 (Jan., 1971), pp. 107-115
- J. García-Cuerva and J. L. Rubio de Francia. Weighted norm inequalities and related topics, 1985.
- David V. Cruz-Uribe, José Maria Martell, and Carlos Pérez. Weights, Extrapolation and the Theory of Rubio de Francia, 2011.
- David Cruz-Uribe, Extrapolation and Factorization, 2017
- Andrei K. Lerner and Fedor Nazarov. Intuitive dyadic calculus: the basics, 2015
- Moen. Sharp weighted bounds without testing or extrapolation. Arch. Math. (Basel) 99 (2012), no. 5, 457–466.
- Muckenhoupt. Weighted norm inequalities for the Hardy maximal function. Transactions AMS, 1972
News
Bonn mathematics performs excellently again in QS ranking
Stefan Schwede is invited speaker at the ECM 2024 in Sevilla
Jessica Fintzen wins Cole Prize
Regula Krapf receives university teaching award
Catharina Stroppel joined the North Rhine-Westphalia Academy for Sciences and Arts
Daniel Huybrechts receives the Compositio Prize for the periode 2017-2019
Catharina Stroppel receives Gottfried Wilhelm Leibniz Prize 2023
Grants for Mathematics students from Ukraine
Jessica Fintzen is awarded a Whitehead Prize of the London Mathematical Society
Peter Scholze elected as Foreign Member of the Royal Society