✦ LIBER ✦
Almost Everywhere Convergence of Inverse Spherical Transforms on Noncompact Symmetric Spaces
✍ Scribed by C. Meaney; E. Prestini
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 428 KB
- Volume
- 149
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
✦ Synopsis
Let G be a connected noncompact semisimple Lie group with finite center and real rank one. Fix a maximal subgroup K. We consider K bi-invariant functions f on G and their spherical transform
where . * denote the elementary spherical functions on GÂK and * 0. We consider the maximal operators
and prove that S* maps boundedly K L K s (G) Ä L s (G)+L 2 (G) for 2nÂ(n+1)<s 2 where n=dim(GÂK ). The result is sharp and it implies a.e. convergence properties of the inverse spherical transforms.