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BCAMSevero Ochoa Award

basque center for applied mathematics

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Roncal Gómez, Luz

Ikerbasque Research and Ramon y Cajal Fellow

Harmonic Analysis

Mazarredo, 14. 48009 Bilbao Basque Country - Spain


Ikerbasque Research and Ramón y Cajal Fellow. My research concerns problems from Harmonic Analysis, Fourier Analysis, Special Functions, and Partial Differential Equations. My first stages of research, starting from my Phd Thesis, are strongly related to the study of classical Harmonic Analysis and Fourier Analysis topics in the context of special functions and orthonormal expansions. Some time after the defense of my Phd, I began to be interested in PDE's problems related to the fractional Laplacian. Spherical means and the solution of the wave equation when the initial data is radial have been others topics in my research. I have also got into some problems related to the so-called sparse domination theory and quantitative estimates for general singular integrals. Moreover, I have been investigating several aspects of discrete Harmonic Analysis and semidiscrete fractional equations. My most recent interests include Hardy inequalities in several settings, such as the Heisenberg group or more general H-type groups, and their applications, as well as their connections with the extension problem. Besides, I am dealing with topics related to Fourier Analysis in the infinite torus. I am also involved in some research concerning unique continuation principles for non-local equations.

Eusko Jaurlaritza - Gobierno Vasco ikerbasque - Basque Foundation for Science Bizkaia xede. Bizkaiko Foru Aldundia innobasque - Agencia vasca de la innovación Universidad del PaÌs Vasco (UPV/EHU)