Hardytype inequalities for fractional powers of the DunklHermite operator
Abstract
We prove Hardytype inequalities for a fractional DunklHermite operator which incidentally give Hardy inequalities for the fractional harmonic oscillator as well. The idea is to use $h$harmonic expansions to reduce the problem in the DunklHermite context to the Laguerre setting. Then, we push forward a technique based on a nonlocal ground representation, initially developed by R. L. Frank, E. H. Lieb and R. Seiringer in the Euclidean setting, to get a Hardy inequality for the fractionaltype Laguerre operator. The abovementioned method is shown to be adaptable to an abstract setting, whenever there is a "good" spectral theorem and an integral representation for the fractional operators involved.
 Publication:

arXiv eprints
 Pub Date:
 February 2016
 DOI:
 10.48550/arXiv.1602.04997
 arXiv:
 arXiv:1602.04997
 Bibcode:
 2016arXiv160204997C
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 Mathematics  Functional Analysis
 EPrint:
 24 pages. Revised version