The aim of this paper is twofold. We first establish the Besov spaces on metric spaces endowed with a doubling measure, via the remarkable orthonormal wavelet basis constructed recently by T. Hytönen and O. Tapiola, and characterize the dual spaces of these Besov spaces. Second, we prove the T1 type theorem for the boundedness of Calderón-Zygmund operators on these Besov spaces. Finally, we introduce a new class of Lipschitz spaces and characterize these spaces via the Littlewood-Paley theory.
|Number of pages||19|
|Journal||Mathematical Methods in the Applied Sciences|
|Publication status||Published - 15 Jul 2017|
- Besov spaces
- Doubling measures
- Metric spaces