V5B8: Selected Topics in Analysis - Weighted inequalities
Summer Semester 2017
- Dr. Pavel Zorin-Kranich
Oral exams take place on August 4 and August 10.
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
- 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,
- David V. Cruz-Uribe, José Maria Martell, and Carlos Pérez.
Weights, Extrapolation and the Theory of Rubio de Francia,
- David Cruz-Uribe,
Extrapolation and Factorization, 2017
- Andrei K. Lerner and Fedor Nazarov.
Intuitive dyadic calculus: the basics,
- 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