My research areas are Harmonic Analysis, Partial Differential Equations, and Geometric Measure Theory. In particular, my research mainly focuses on the Calderon-Zygmund theory, the weighted norm inequalities, and the elliptic PDE with rough coefficients in rough domains.
M. Cao, P. Hidalgo-Palencia, J.M. Martell, C. Prisuelos-Arribas, and Z. Zhao, Elliptic operators in rough sets and the Dirichlet problem with boundary data in Hölder spaces, J. Funct. Anal. 288 (2025), 110801.
M. Cao, K. Yabuta, Absolute continuity of degenerate elliptic measure, J. Funct. Anal. 288 (2025), 110673.
M. Cao, P. Hidalgo-Palencia, and J.M. Martell, Carleson measure estimates, corona decompositions, and perturbation of elliptic operators without connectivity, Math. Ann. 390 (2024), 95-156.
M. Cao, G. Ibañez-Firnkorn, I.P. Rivera-Ríos, Q. Xue, and K. Yabuta, A class of multilinear bounded oscillation operators on measure spaces and applications, Math. Ann. 388 (2024), 3627-3755.
M. Cao, K. Yabuta, and D. Yang, A compact extension of Journe's T1 theorem on product spaces, Trans. Amer. Math. Soc. 377 (2024), 6251-6309.
M. Cao, J. J. Marin, and J. M. Martell, Extrapolation on function and modular spaces, and applications, Adv. Math. 406 (2022), 108520.
M. Cao, O. Dominguez, J.M. Martell, and P. Tradacete, On the $A_{\infty}$ condition for elliptic operators in 1-sided NTA domains satisfying the capacity density condition, Forum Math. Sigma, 10 (2022), e59, 1-57.
M. Cao, A. Olivo, and K. Yabuta, Extrapolation for multilinear compact operators and applications, Trans. Amer. Math. Soc. 375 (2022), 5011-5070.
M. Cao, Q. Xue, and K. Yabuta, Weak and strong type estimates for the multilinear pseudo-differential operators, J. Funct. Anal. 278 (2020), 108454.
M. Cao, Q. Xue, and K. Yabuta, On multilinear fractional strong maximal operator associated with rectangles and multiple weights, Rev. Mat. Iberoam. 33 (2017), 555-572.
M. Cao and K. Yabuta, A compact multilinear T1 theorem on product spaces, (2024), https://arxiv.org/abs/2410.10304.
M. Cao, H. Liu, Z. Si, and K. Yabuta, A characterization of compactness via bilinear T1 theorem, (2024), https://arxiv.org/abs/2404.14013.
M. Cao, J. Chen, Z. Li, F. Liao, K. Yabuta, J. Zhang, A compact T1 theorem for singular integrals associated with Zygmund dilations, (2023), https://arxiv.org/abs/2307.13932.