A Battle-Lemarié Frame Characterization of Besov and Triebel-Lizorkin Spaces
Abstract
Abstract In this paper, we investigate a spline frame generated by oversampling against the well-known Battle-Lemarié wavelet system of nonnegative integer order, n . We establish a characterization of the Besov and Triebel-Lizorkin (quasi-) norms for the smoothness parameter up to $$s < n+1$$ s < n + 1 , which includes values of s where the Battle-Lemarié system no longer provides an unconditional basis; we, additionally, prove a result for the endpoint case $$s=n+1$$ s = n + 1 . This builds off of earlier work by G. Garrigós, A. Seeger, and T. Ullrich, where they proved the case $$n=0$$ n = 0 , i.e. that of the Haar wavelet, and work of R. Srivastava, where she gave a necessary range for the Battle-Lemarié system to give an unconditional basis of the Triebel-Lizorkin spaces.
Fields of Study & Subjects
Mathematical Analysis and Transform Methods
Advanced Harmonic Analysis Research
Approximation Theory and Sequence Spaces
Publication details
- Journal / source
- Journal of Fourier Analysis and Applications
- Publisher
- Springer Science and Business Media LLC
- Volume
- 32
- Issue
- 3
- Publication date
- 20 April 2026
- Language
- EN