Let X=GรK be a noncompact symmetric space of real rank one. The purpose of this paper is to investigate L p boundedness properties of a certain class of radial Fourier integral operators on the space X. We will prove that if u { is the solution at some fixed time { of the natural wave equation on X
Vector-valued Fourier multipliers on symmetric spaces of the noncompact type
โ Scribed by Leszek Skrzypczak
- Publisher
- Springer Vienna
- Year
- 1995
- Tongue
- English
- Weight
- 860 KB
- Volume
- 119
- Category
- Article
- ISSN
- 0026-9255
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
On a symmetric space X=GรK of noncompact type, we consider the formulas where 8 \* is the spherical function on X. Taken together they represent, the synthesis and decomposition formulas for appropriate functions f on X in terms of joint eigenfunctions of the invariant differential operators on X.
We study the decay of the FOURIER-coefficients of vector-valued functions F :T --+ X, X a BANAFH space. Differentiable functions f generally have absolutely sumrnable FOURIER-coefficients, 1 Ilf(n)ll < 00, iff X is K-convex. More precise statements on the decay of Ilf(n)ll for regular functions fcan