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Hardy-Type Inequalities for Fractional Powers of the Dunkl–Hermite Operator
| Content Provider | Scilit |
|---|---|
| Author | Ciaurri, Óscar Roncal, Luz Thangavelu, Sundaram |
| Copyright Year | 2018 |
| Description | We prove Hardy-type inequalities for a fractional Dunkl–Hermite operator, which incidentally gives Hardy inequalities for the fractional harmonic oscillator as well. The idea is to useh-harmonic expansions to reduce the problem in the Dunkl–Hermite context to the Laguerre setting. Then, we push forward a technique based on a non-local ground representation, initially developed by Franket al. [‘Hardy–Lieb–Thirring inequalities for fractional Schrödinger operators,J. Amer. Math. Soc.21(2008), 925–950’] in the Euclidean setting, to obtain a Hardy inequality for the fractional-type Laguerre operator. The above-mentioned 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. |
| Related Links | http://bird.bcamath.org/bitstream/20.500.11824/920/1/CRT-PEMS.pdf https://www.cambridge.org/core/services/aop-cambridge-core/content/view/71DFE4DC547D3201CB2798A0D2B3DB1B/S0013091517000311a.pdf/div-class-title-hardy-type-inequalities-for-fractional-powers-of-the-dunkl-hermite-operator-div.pdf |
| Ending Page | 544 |
| Page Count | 32 |
| Starting Page | 513 |
| ISSN | 00130915 |
| e-ISSN | 14643839 |
| DOI | 10.1017/s0013091517000311 |
| Journal | Proceedings of the Edinburgh Mathematical Society |
| Issue Number | 2 |
| Volume Number | 61 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2018-05-01 |
| Access Restriction | Open |
| Subject Keyword | Proceedings of the Edinburgh Mathematical Society Mathematical Physics Hardy Inequality Dunkl Harmonic Oscillator Fractional Order Operator Laguerre Expansions Heat Semigroup Primary 26a33 Secondary 33c45 |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
