Abstract
In this article, we study the boundedness properties of the averaging operator S γt on Triebel-Lizorkin spaces \(\dot F_{p,q}^\alpha \left( {{\mathbb{R}^n}} \right)\) for various p,q. As an application, we obtain the norm convergence rate for S γt (f) on Triebel-Lizorkin spaces and the relation between the smoothness imposed on functions and the rate of norm convergence of S γt is given.
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Supported by the National Natural Science Foundation of China(12071437, 12101562), the Natural Science Foundation of Zhejiang(LQ20A010003) and the Natural Science Foundation from the Education Department of Anhui Province(KJ2017A847).
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Zhao, Jy., Pan, Yl. Certain averaging operators on Triebel-Lizorkin spaces. Appl. Math. J. Chin. Univ. 37, 546–562 (2022). https://doi.org/10.1007/s11766-022-4035-3
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DOI: https://doi.org/10.1007/s11766-022-4035-3