Profile
I am a lecturer at the Department of Applied Mathematics at Santa Clara University working in the field of Harmonic Analysis.
Education and Employment
I graduated with a Ph. Degree in Mathematics from the University of Valencia, Spain
I have held academic positions at the University of Valencia, the University of Edinburgh (UK), the University of Glasgow (UK), Lund University (Sweden), the University of California Los Angeles, the University of Georgia, Temple University, California Polytechnic State University, and currently at Santa Clara University.
Research interests
My research interests focus on Harmonic Analysis and its applications to the study of Partial Differential Equations (PDEs).
In Harmonic Analysis, I work on Time-Frequency Analysis, Singular Integration, T1 Theory, and compact Calderón-Zygmund operators.
In the field of PDEs, I study dispersive and elliptic equations, the Schrodinger and Wave maximal operators, the Cauchy Integral operator over Lipschitz paths and the Double Layer Potential operator.
Teaching
Recently I have been lecturing the courses Differential Equations Amth106, Probability and Statistics Amth 108, Risk Analysis Amth 112, and Numerical Methods Amth 118.
Selected Publications
- Stockdale C., Villarroya P., Wick B., Sparse domination results for compactness on weighted spaces. Collect. Math, 73, 3, (2022), 535-563
- Villarroya P., A global Tb Theorem for boundedness and compactness of Calderon-Zygmund operators, J. Math. Anal. Appl., 480, 1, (2019)
- Olsen J.F., Villarroya P., Endpoint estimates for compact Calderon-Zygmund operators. Revista Matematica Iberoamericana, Vol. 33, No. 4, (2017)
- Villarroya P., A characterization of compactness for singular integrals. Journal de Mathematiques Pures et Appliquees, 104, 3, (2015)
- Benyi A., Demeter C., Nahmod A., Thiele C., Torres R., Villarroya P., Modulation invariant bilinear T(1) theorem. J. Anal. Math., 109 (2009)
