skip to content

Hardy-type inequalities for fractional powers of the Dunkl--Hermite operator

Presented by: 
Luz Roncal
Monday 8th April 2019 - 15:00 to 16:00
INI Seminar Room 2
We prove Hardy-type inequalities for the conformally invariant fractional powers of the Dunkl--Hermite operator. Consequently, we also obtain Hardy inequalities for the fractional harmonic oscillator as well.
The strategy is as follows: first, by introducing suitable polar coordinates, we reduce the problem to the Laguerre setting. Then, we push forward an argument developed by R. L. Frank, E. H. Lieb and R. Seiringer, initially developed in the Euclidean setting, to get a Hardy inequality for the fractional-type Laguerre operator. Such argument is based on two facts: first, to get an integral representation for the corresponding fractional operator, and second, to write a proper ground state representation.
This is joint work with \'O. Ciaurri (Universidad de La Rioja, Spain) and S. Thangavelu (Indian Institute of Science of Bangalore, India).
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons