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 Ap 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 Ap; 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