Title: Boundedness properties for Hermite pseudo-multipliers 

Abstract: Fourier multipliers and pseudo-differential operators are defined by means of the Fourier transform and play an important role in the study of partial differential equations. In the same spirit, Hermite pseudo-multipliers are associated to Hermite expansions and they represent the counterparts to pseudo-differential operators in the Hermite setting. 

After some preliminaries, we will present results on boundedness properties of pseudo-multipliers in function spaces associated to the Hermite operator. The main tools in the proofs involve new molecular decompositions and molecular synthesis estimates for Hermite Besov and Hermite Triebel-Lizorkin spaces, which allow to obtain boundedness results on spaces for which the smoothness allowed includes non-positive values. In particular, we obtain boundedness results for pseudo-multipliers on Lebesgue and Hermite local Hardy spaces.

The talk is based on joint work with Fu Ken Ly (The University of Sydney).

About the Speaker: Virginia Naibo earned her undergraduate degree, or Licenciatura, in mathematics from Universidad Nacional de Rosario and her PhD in 2002 from Universidad Nacional del Litoral, Argentina under the supervision of Hugo Aimar and Liliana Forzani.  She held a three-year postdoctoral position at the University of Kansas and was a tenure-track assistant professor at Rose-Hulman Institute of Technology for a year before joining the faculty of the mathematics department at Kansas State University, where she is professor and associate department head. Naibo’s research interests are in the area of Fourier analysis. Her more recent work concerns the study of different aspects of linear and bilinear pseudodifferential operators and singular integrals, Leibniz-type rules, commutator estimates and function spaces, among other topics. Applications of her work to analysis and partial differential equations include pointwise multiplication properties of function spaces, well-posedness results for Euler, Navier-Stokes and Korteweg-de Vries equations as well as for the Ideal Magneto Hydrodynamic equations, smoothing properties of Schrödinger semigroups, and scattering properties of solutions to systems of partial differential equations associated to local and nonlocal operators. Naibo’s research in Fourier Analysis has been funded by grants from the NSF and the Simons Foundation and her work has been published in internationally recognized journals. She has delivered numerous invited lectures in the U.S. and abroad. Naibo's teaching accomplishments have been recognized through nominations for teaching awards at the college and university levels. Naibo has contributed to the integration of research and education at the postdoctoral, graduate and undergraduate levels. She was the doctoral advisor of three graduate students and the mentor of a postdoctoral fellow, who are all successfully placed in academic positions. She has supervised several undergraduate research projects in topics such as the development of Fourier analysis techniques in digital image processing as well as in interdisciplinary collaborations in chemistry and mathematics. Most of these students have continued to pursue doctoral degrees in STEM disciplines.