Higher order Riesz transforms,fractional derivatives,and Sobolev spaces for Laguerre expansions |
| |
| Institution: | 1. Département de mathématiques, université d''Angers, 2, boulevard Lavoisier, 49045 Angers Cedex 01, France;2. Departamento de Matemáticas, Facultad de Ciencias, UCV. Aptd 47195 Los Chaguaramos, Caracas 1041-A, Venezuela;3. Institute of Mathematics, Wroclaw University of Technology, Wyb. Wyspiańskiego 27, 50-370 Wroclaw, Poland |
| |
| Abstract: | We study different Sobolev spaces associated with multidimensional Laguerre expansions. To do this we establish an analogue of P.A. Meyer's multiplier theorem, prove some transference results between higher order Riesz–Hermite and Riesz–Laguerre transforms, and introduce fractional derivatives and integrals corresponding to the Laguerre setting. Hypercontractivity of the Laguerre semigroups and Calderón's reproduction formula are also discussed. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
