## Research

## Publications

- A new look at subrepresentation formulas, submitted, with C. Hoang and C. Pérez.
- Degenerate parabolic p-Laplacian equations: existence, uniqueness and asymptotic behavior of solutions, submitted, with D. Cruz-Uribe and Y. Zhao.
- New pointwise bounds by Riesz potential type operators, submitted, with C. Hoang and C. Pérez.
- A homage to Guido Weiss and his leadership of the Saint Louis team: Commutators of singular integrals and Sobolev inequalities, to appear in a special volume dedicated to Guido Weiss, Birkhauser/Springer series, with C. Hoang and C. Pérez.
- Bump conditions for general iterated commutators with applications to compactness, to appear Illinois J. Math., with A. Mair and Y. Wen.
- Pointwise estimates for rough operators with applications to Sobolev inequalities, to appear J. D'Analyse, with C. Hoang and C. Pérez.
- Two weight bump conditions for compactness of commutators, Arch. Math. (Basel) 120 (2023) 47-57, with A. Mair.
- New oscillation classes and two weight bump conditions for commutators, Collect. Mat., 74 (2023), 225–246, with D. Cruz-Uribe and Q. Minh Tran.
- Weak endpoint bounds for matrix weights, Rev. Mat. Iberoam. 37 (2021), 1513-1538, with D. Cruz-Uribe, J. Isralowitz, S. Pott, and I. Rivera-Rios.
- A multilinear reverse Hölder inequality with applications to multilinear weighted norm inequalities, Georgian Math. J. 27 (2020), 37-42, with D. Cruz-Uribe.
- A new approach to norm inequalities on weighted and variable Hardy spaces, Ann. Acad. Sci. Fenn. 45 (2020) 175-198, with D. Cruz-Uribe and H. Nguyen.
- Boundedness results for commutators with BMO functions via weighted estimates: a comprehensive approach, Math. Ann. 376 (2020), 853-871, with Á. Bényi, J. M. Martell, E. Stachura, R.H. Torres.
- Multilinear fractional Calderon-Zygmund operators on weighted Hardy spaces, Houston Math. J. 45 (2019), 679-713, with D. Cruz-Uribe and H. Nguyen.
- Matrix weighted Poincaré inequalities and applications to degenerate elliptic systems, Indiana Univ. Math. J. 68 (2019) 1327-1377, with J. Isralowitz.
- The boundedness of multilinear Calderón-Zygmund operators on weighted and variable Hardy spaces, Pub. Mat. 63 (2019) D. Cruz-Uribe and H. Nguyen.
- Two weight bump conditions for matrix weights, Integral Equations Operator Theory, 90 (2018), 31 pp., with D. Cruz-Uribe and J. Isralowitz.
- Extrapolation in the scale of generalized reverse Hölder weights, Rev. Complut. Mat., 31 (2018), 263–286 with T. Anderson and D. Cruz-Uribe.
- Weighted estimates for bilinear fractional integral operators and their commutators Indiana Univ. Math. J., 67 (2018) 397–428, with C. Hoang.
- On the harmonic and geometric maximal operators associated to a general basis, Math. Inequal. Appl., 21 (2018) 265-286, with L. Anne Duffee.
- Muckenhoupt-Wheeden conjectures for sparse operators, Arch. Math. (Basel), 109 (2017) 49-58, with C. Hoang.
- Matrix \(A_p\) weights, degenerate Sobolev spaces, and mappings of finite distortion, J. Geom. Anal., 26 (2016) 2797–2830, with D. Cruz-Uribe and S. Rodney.
- Unions of Lebesgue spaces and \(A_1\) majorants, Pacific J. Math. 280 (2016), 411-432, with G. Knese and J. McCarthy.
- Regularity for weak solutions of elliptic PDE below the natural exponent, Ann. Mat. Pura Appl, 195 (2016) 725-740, with D. Cruz-Uribe and S. Rodney.
- Compactness properties of commutators of bilinear fractional integrals, Math. Z. 280 (2015) 569-582, with A. Benyi, W. Damien, and R.H. Torres.
- Sharp weighted inequalities for multilinear fractional maximal operators and fractional integrals, Math. Nachr. 288 (2015) 619-632, with K. Li and W. Sun.
- Compact bilinear operators: the weighted case, Michigan Math. J. 64 (2015) 39-51, with A. Benyi, W. Damien, and R.H. Torres.
- Logarithmic bump conditions for Calderón-Zygmund operators on spaces of homogeneous type, Publ. Mat. 59 (2015) 17-43, with T. Anderson and D. Cruz-Uribe.
- The sharp weighted bound for multilinear maximal functions and Calderón-Zygmund operators, J. Fourier Anal. and Appl. 20 (2014) 751-765, with K. Li and W. Sun.
- Bilinear Sobolev-Poincaré inequalities and Leibniz-type rules, J. Geom. Anal. 24 (2014) 1144-1180, with F. Bernicot, D. Maldonado, and V. Naibo.
- Higher-order multilinear Poincare and Sobolev inequalities in Carnot groups, Potential Anal. 40 (2014) 231-245, with V. Naibo.
- New weighted estimates for bilinear fractional integral operators, Trans. Amer. Math. Soc. 366 (2014) 627-646.
- One and two weight norm inequalities for Riesz potentials, Illinois J. Math. 57 (2013) 295-323, with D. Cruz-Uribe.
- Mixed \(A_p-A_\infty\) estimates with one supremum, Studia Math. 219 (2013) 247-267, with A. Lerner.
- A panorama of sampling theory, Excursions in harmonic analysis. Volume 1, 107-127, Appl. Numer. Harmon. Anal. Birkhauser/Springer, New York 2013, with H. Sikic, G. Weiss, and E. Wilson.
- A fractional Muckenhoupt-Wheeden theorem and its consequences, Integral Equations Operator Theory 76 (2013) 421-446, with D. Cruz-Uribe.
- Regularity of solutions to degenerate \(p\)-Laplacian equations, J. Math. Anal. Appl. 401 (2013) 458-478, with D. Cruz-Uribe and V. Naibo.
- Sharp weighted bounds without testing or extrapolation, Arch. Math. 99 (2012) 457-466.
- Sharp norm inequalities for commutators of classical operators, Publ. Mat. 56 (2012) 147-190, with D. Cruz-Uribe.
- Weighted multilinear Poincaré inequalities for vector fields of Hormander type, Indiana Univ. Math. J. 60 (2011) 473-506, with D. Maldonado and V. Naibo.
- Multiparameter weights with connections to Schauder bases, J. Math. Anal. Appl. 371 (2010) 266-281.
- Sharp weighted bounds for fractional integral operators, J. Funct. Anal. 259 (2010) 1073-1097, with M. Lacey, C. Pérez, and R.H. Torres.
- Sharp one-weight and two-weight bounds for maximal operators, Studia Math. 194 (2009) 163-180.
- Weighted inequalities for multilinear fractional integral operators, Collect. Math. 60 (2009) 213-238.