Mathematical Institute of the University of Bonn

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.

1. Fefferman-Stein inequality
2. The A_p condition
3. Extrapolation, sparse operators
4. Calderón-Zygmund operators
5. Calderón-Zygmund operators, continued
6. May 26: sparse domination for a nontangentional maximal operator
7. June 2: A_∞ and the reverse Hölder inequality
8. June 23: mixed A_∞ estimates
9. June 30: intrinsic square function, only Section 2 without Lemma 2.2 and with v=1, beta=1.
10. July 7: Embedding A_∞ into A_p; Orlicz spaces
11. July 14: Fefferman-Stein type inequality for sparse operators, following this article, another proof of sparse domination following this article
12. 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