✦ LIBER ✦
On Hardy-Bessel Potential Spaces Over the 2-Series Field
✍ Scribed by Jun Tateoka
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 650 KB
- Volume
- 168
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
The purpose of this paper is to present characterizations of the inhomogeneous Hardy‐Bessel potential spaces F^p^~α~ (K) over the 2‐series field K defined by Littlewood‐Paley type function, magnified image where Δ~0~(x) = 1(|x|≥1), = 0(other), Δ~j~(x) = 2^j^ ≥, = 0(other) (j ≥ 1). These characterizations are given by difference of functions, ball means of difference and atoms. As applications of these results we shall determine when F^p^~α~(K) is a multiplication algebra, and prove the lower majorant property, the uniform localization property and the equivalence of Fourier multipliers.