Research

Publications

1. Carleson perturbations for the regularity problem (with Z. Dai and S. Mayboroda), Rev. Mat. Iberoam., accepted. (arXiv)

2. Elliptic theory in domains with boundaries of mixed dimension (with G. David and S. Mayboroda), Astérisque, accepted. (arXiv)

3. Absolute continuity of the harmonic measure on low dimensional rectifiable sets, J. Geom. Anal., accepted. (arXiv)

4. Green function estimates on complements of low-dimensional uniformly rectifiable sets (with G. David and S. Mayboroda), Math. Ann., accepted. (arXiv)

5. Generalized Carleson perturbations of elliptic operators and applications (with B. Poggi), Transactions of the AMS, accepted. (arXiv)

6. Green function with pole at infinity applied to the study of the elliptic measure,  Anal. PDE, accepted. (arXiv)

7. A change of variable for Dahlberg-Kenig-Pipher operators, Proceedings of the AMS 150, 3565-3579 , 2022. (arXiv)

8. The Dirichlet problem in domains with lower dimensional boundaries (with S. Mayboroda and Z. Zihui), Rev. Mat. Iberoam. 37, no. 3, 821–910, 2021. (arXiv)

9. A new elliptic measure in lower dimensional sets (with G. David and S. Mayboroda), Acta Math. Sinica, special issue in honor of Carlos Kenig’s 65th birthday, 35, no 6, 876–902, 2019. (arXiv)

10. Dahlberg’s theorem in higher co-dimension (with G. David and S. Mayboroda), J. Funct. Anal. 276, no 9, 2731–2820, 2019. (arXiv)

11. Elliptic theory for sets with higher co-dimensional boundaries (with G. David and S. Mayboroda). Mem. Amer. Math. Soc. 274, no 1346, 2021. (arXiv)

12. Algebra properties for Besov spaces on unimodular Lie groups. Colloq. Math. 154, 205–240, 2018. (arXiv)

13. About the L2-analyticity of Markov operators on graphs. Proc. Amer. Math. Soc. 146, 1793–1805, 2018. (arXiv)

14. Harmonic measure on sets of codimension larger than one (with G. David and S. Mayboroda), C. R. Math. Acad. Sci. Paris 355, no. 4, 406–410, 2017. (arXiv)

15. Riesz transform for 1 ≤ p ≤ 2 without Gaussian heat kernel bound (with L. Chen, T. Coulhon, and E. Russ), J. Geom. Anal., 27, no 2, 1489–1514, 2017. (arXiv)

16. Hardy and BMO spaces on graphs, application to Riesz transform, Pot. Anal. 45, no 1, 1–54, 2016. (arXiv)

17. Littlewood-Paley functionals on graphs, Math. Nachr. 288 11-12, 1254–1285, 2015. (arXiv)

Preprints

18. Comparison between Green functions and smooth distances (with L. Li and S. Mayboroda), see arXiv.

19. The regularity problem in domains with lower dimensional boundaries (with Z. Dai and S. Mayboroda), see arXiv.

20. Boundedness of Riesz transform on H1 under sub-Gaussian estimates, see arXiv.

In Preparation

21. The comparison principle implies that the domain is uniform.