Abstract
Based on the role of the polynomial functions on the homogeneous Besov spaces, on the homogeneous Triebel-Lizorkin spaces and on their realized versions, we study and obtain characterizations of these spaces via difference operators in a certain sense.
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Acknowledgements
I would like to thank Gérard Bourdaud, University of Paris Diderot, for his help and his remarks. Thanks are also due to the referees for their valuable comments and suggestions.
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Moussai, M. Characterizations of realized homogeneous Besov and Triebel-Lizorkin spaces via differences. Appl. Math. J. Chin. Univ. 33, 188–208 (2018). https://doi.org/10.1007/s11766-018-3431-1
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DOI: https://doi.org/10.1007/s11766-018-3431-1
Keywords
- homogeneous Besov space
- homogeneous Triebel-Lizorkin space
- Nikol’skij representation method
- realizations
- Hardy estimates