Dr. Dorothee Frey

Research Interests

Harmonic analysis and operator theory with applications to PDEs

Publications

  1. (With F. Bernicot) Riesz transforms through reverse Hölder and Poincaré inequalities.
    Mathematische Zeitschrift 284, 791–826 (2016).
    Preprint: arXiv:1503.02508.

  2. (With F. Bernicot, S. Petermichl) Sharp weighted norm estimates beyond Calderón-Zygmund theory.
    Analysis & PDE 9, No. 5, 1079-1113 (2016).
    Preprint: arXiv:1510.00973.

  3. (With A. McIntosh, P. Portal) Conical square function estimates and functional calculi for perturbed Hodge-Dirac operators in L^p.
    Accepted for publication in Journal d'Analyse Mathématique (2016).
    Preprint: arXiv:1407.4774.

  4. (With F. Bernicot, T. Coulhon) Sobolev algebras through heat kernel estimates.
    Journal de l'École polytechnique — Mathématiques 3, 99-161 (2016).
    Available at jep.cedram.org.

  5. Appendix to I. Bailleul, F. Bernicot, Heat semigroup and singular PDEs.
    Journal of Functional Analysis 270 (no. 9), 3344–3452 (2016).
    Preprint: arXiv:1501.06822.

  6. (With F. Bernicot, T. Coulhon) Gaussian heat kernel bounds through elliptic Moser iteration.
    Journal de Mathématiques Pures et Appliquées (9) 106, No. 6, 995-1037 (2016). DOI: 10.1016/j.matpur.2016.03.019.
    Preprint: arXiv:1407.3906 .

  7. (With P. Auscher) On the well-posedness of parabolic equations of Navier-Stokes type with BMO^{-1} data.
    Journal of the Institute of Mathematics of Jussieu. FirstView (2015). DOI: 10.1017/S1474748015000158.
    Preprint: arXiv:1412.8407.

  8. (With F. Bernicot) Pseudodifferential operators associated with a semigroup of operators.
    Journal of Fourier Analysis and Applications 20 (no. 1), 91–118 (2014). Preprint: arXiv:1212.2349.

  9. Paraproducts via H^\infty-functional calculus.
    Revista Matematica Iberoamericana 29 (no. 2), 635-663 (2013). Preprint: arXiv:1107.4348.

  10. (With P. C. Kunstmann) A T(1)-Theorem for non-integral operators.
    Mathematische Annalen 357 (no. 1), 215-278 (2013). Preprint: arXiv:1107.4347.

Preprints

  1. (With F. Bernicot) Sobolev algebras through a "carré du champ" identity.
    Available at arXiv:1612.00280 (2016)

  2. (With I. Bailleul, F. Bernicot) Higher order paracontrolled calculus and 3d-PAM equation.
    Available at arXiv:1506.08773 (2015).

Thesis

Paraproducts via H^\infty-functional calculus and a T(1)-Theorem for non-integral operators, KIT Karlsruhe, 2011 (http://digbib.ubka.uni-karlsruhe.de/volltexte/1000022796).