# Learning seminars on Harmonic Analysis related to PDEs

## Goal

The goal of this learning seminar is to study harmonic analysis tools that are closely related to the theory of PDEs.

## Time/Venue

We will meet Tuesday from 4 PM – 5:30 PM at 205 Kassar House.

## Schedule

Date | Topic | Refs | Speakers |
---|---|---|---|

Sep/20 | Organizational meeting | ||

Sep/27 | Calderon-Zygmund decomposition and $L_p$-boundedness of singular integrals | 1,7,11 | Will |

Oct/04 | Application of Calderon-Zygmund decomposition, John-Nirenberg theorem | 1,12 | Will |

Oct/11 | Introduction to sparse operators(guest lecture) | Jose | |

Oct/18 | $A_p$-weights (Reverse Holder inequality, Singular integrals) | 5,12 | Tainara |

Oct/25 | $A_p$-weights (Rubio de Francia extrapolation) | 2,3 | Nathan |

Nov/1 | Littlewood-Paley square function theorem | 5,9 | Hanye |

Nov/8 | No seminar (Election day) | ||

Nov/15 | Commutator estimates (Coifman-Rosenberg-Weiss) | 6,8 | Nathan |

Nov/22 | Paraproducts and Coifman-Meyer theorem | 6,10 | Will |

Nov/29 | Strichartz estimates for Schrodinger equations | 12 | Haram |

Dec/6 | Strichartz estimates for wave equations | 12 | Bruno |

## Notes

## References

- L. A. Caffarelli and I. Peral, On $W^{1,p}$ estimates for elliptic equations in divergence form, Comm. Pure Appl. Math. 51 (1998), no.1, 1–21.
- H. Dong and D. Kim, On $L_p$-estimates for elliptic and parabolic equations with $A_p$ weights, Trans. Amer. Math. Soc. 370 (2018), no. 7, 5081–5130.
- J. Duoandikoetxea, Fourier analysis, GSM, vol 29, AMS, Providence, RI, 2001.
- M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems, Annals of Mathematics Studies, Vol. 105, Princeton University Press, Princeton, NJ, 1983.
- L. Grafakos, Classical Fourier analysis, 3rd Edition, GTM, vol. 249, Springer, New York, 2014.
- L. Grafakos, Modern Fourier analysis, 3rd Edition, GTM, vol. 249, Springer, New York, 2014.
- N. V. Krylov, Lectures on elliptic and parabolic equations in Sobolev spaces, GSM, vol. 96, AMS, Providence, RI, 2008.
- D. Li, On Kato-Ponce and fractional Leibniz, Rov. Math. Iberoam. 35 (2019), 23–100.
- C. Muscalu and W. Schlag, Classical and multilinear harmonic analysis, Vol. I, Cambridge University Press, Cambridge, 2013.
- C. Muscalu and W. Schlag, Classical and multilinear harmonic analysis, Vol. II, Cambridge University Press, Cambridge, 2013.
- E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30., Princeton University Press, Princeton, N.J., 1970.
- E. M. Stein, Harmonic analysis: real-variable methods, orthogonality, andPrinceton Mathematical Series, vol.~43, Princeton University Press, Princeton, NJ, 1993, With the assistance of Timothy S. Murphy, Monographs in Harmonic Analysis, III.