My field of research is Harmonic Analysis. I study the properties of singular integral operators such as the Cauchy integral, and the double layer potential operators. The main tools I use are time-frequency analysis (wavelets, and wave-packets decompositions), the T1 theory, and Calderón-Zygmund theory.
I also develop applications to the study of partial differential equations, mostly in the setting of Potential Theory and dispersive equations, and Numerical Methods, in particular to the design of algorithms for the fast evaluation of dense matrices.
This is the list of my research papers:
In preparation:
Boundedness and compactness of pseudo-differential operators with rough symbols.
A local Tb theorem for compactness on non-homogeneous spaces.
On the dualization of compact weak type estimates, with J.F. Olsen.
Fast wavelet transforms of compact singular integrals, with G. Tierra Chica.
Published or submitted for publication:
Sparse domination of singular bilinear forms on non-homogeneous spaces. Submitted
New local T1 Theorems on non-homogeneous spaces. Accepted in Publicacions Matemàtiques (2024)
The Schatten classes of Calderón-Zygmund operators, Journal of Fourier Analysis and Applications, 30, 9 (2024)
Sparse domination results for compactness on weighted spaces, with C. Stockdale and B. Wick, Collectanea Mathematica, 73, 3, (2022), 535-563
A global Tb Theorem for boundedness and compactness of Calderón-Zygmund operators, J. Math. Anal. Appl., 480, 1, (2019), arxiv
Endpoint compactness of singular integrals and perturbations of the Cauchy Integral, pdf arxiv with K-M Perfekt, and S. Pott, Kyoto Journal of Mathematics, 7, 2, (2017), 365-393.
Endpoint estimates for compact Calderón-Zygmund operators, pdf arxiv with J.F. Olsen. Revista Matemática Iberoamericana, 33, 4, (2017), 1285-1308.
A characterization of compactness for singular integrals, pdf arxiv Journal de Mathématiques Pures et Appliquées, 104, 3, (2015), 485-532.
Off-diagonal and pointwise estimates for compact Calderón-Zygmund operators, pdf arxiv Methods of Fourier Analysis and Approximation Theory, 85-112, part of the Applied and Numerical Harmonic Analysis book series (ANHA) (2015).
A T(1) theorem on product spaces, pdf with S. Pott.
Transference of vector-valued multipliers on weighted L^p-spaces, pdf with O. Blasco, Canadian Journal of Mathematics, 65 (3), (2013), 510-543.
On boundedness of discrete multilinear singular integral operators, pdf arxiv J. Math. Anal. Appl., 382, (2011), 534-548.
Modulation invariant bilinear T(1) theorem, pdf arxiv with A. Benyi, C. Demeter, A. Nahmod, C. Thiele, and R. Torres, J. Anal. Math., 109 (2009), 279-352.
Bilinear multipliers on Lorentz spaces, pdf arxiv Czechoslovak Math. J., 58 (133), (2008), 4, 1045-1057.
Sharp estimates for maximal operators associated to the wave equation, pdf arxiv with K. Rogers, Ark. Math., 46, (2008), 1, 143-151.
Global estimates for the Schrodinger maximal operator, pdf with K. Rogers, Ann. Acad. Sci. Fenn., 32, (2007), 2, 425-435.
Commutators of bilinear and linear Hilbert transforms pdf with O. Blasco, Proc. Amer. Math. Soc. 132 (2004), 7, 1997-2004.
Transference of bilinear multiplier operators on Lorentz spaces pdf arxiv with O. Blasco, Illinois J. Math. 47 (2003), 4, 1327-1343.