Hardy-type inequalities for fractional Powers of the Dunkl-Hermite operator. (English) Zbl 1435.26013
Hardy-type inequalities for a fractional Dunkl-Hermite operator are derived, proved and discussed. The method of \(h\)-harmonic expansions was used to reduce the problem of the Dunkl-Hermite to the Laguerre setting and thereafter the forward technique approach which is based on the non-local ground representation in the Euclidean setting was employed to obtain the Hardy-type inequality for fractional type Laguerre operator. Several consequences of the results obtained are pointed out and well discussed.
Reviewer: James Adedayo Oguntuase (Abeokuta)
MSC:
| 26D10 | Inequalities involving derivatives and differential and integral operators |
| 26A33 | Fractional derivatives and integrals |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 35A08 | Fundamental solutions to PDEs |
| 42C10 | Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) |
| 43A90 | Harmonic analysis and spherical functions |
Keywords:
Hardy inequality; Dunkl harmonic oscillator; fractional order operator; Laguerre expansions; heat semigroupSoftware:
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