V5B8: Weighted inequalities, summer term 2017 - Mathematisches Institut der Universität Bonn

V5B8: Selected Topics in Analysis - Weighted inequalities

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 A_p 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 A_p; 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, 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