Boggarapu, Pradeep and Roncal, Luz and Thangavelu, Sundaram (2019) ON EXTENSION PROBLEM, TRACE HARDY AND HARDY'S INEQUALITIES FOR SOME FRACTIONAL LAPLACIANS. In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 18 (5). pp. 2575-2605.
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We obtain generalised trace Hardy inequalities for fractional powers of general operators given by sums of squares of vector fields. Such inequalities are derived by means of particular solutions of an extended equation associated to the above-mentioned operators. As a consequence, Hardy inequalities are also deduced. Particular cases include Laplacians on stratified groups, Euclidean motion groups and special Hermite operators. Fairly explicit expressions for the constants are provided. Moreover, we show several characterisations of the solutions of the extension problems associated to operators with discrete spectrum, namely Laplacians on compact Lie groups, Hermite and special Hermite operators.
| Item Type: | Journal Article |
|---|---|
| Publication: | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS |
| Publisher: | AMER INST MATHEMATICAL SCIENCES-AIMS |
| Additional Information: | Copyright of this belongs to AMER INST MATHEMATICAL SCIENCES-AIMS |
| Keywords: | Trace Hardy inequality; Hardy's inequality; extension problem; characterisation of solutions; fractional Laplacian |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 27 May 2019 07:40 |
| Last Modified: | 27 May 2019 07:40 |
| URI: | http://eprints.iisc.ac.in/id/eprint/62310 |
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