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Boundedness of Iterated Spherical Average on α-Modulation Spaces

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Abstract

For the iteration of spherical average (A1)N and the Laplace operator Δ, we consider the boundedness of the operator Δ(A1)N on the α-modulation spaces \(M_{p,q}^{s,\alpha }\). The authors obtain some sufficient and necessary conditions to ensure the boundedness on the α-modulation spaces. The main theorems significantly improve some known results.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, China

    Qiang Huang

  2. College of Data Science, Jiaxing University, Jiaxing, Zhejiang, 314001, China

    Xiaomei Wu

Authors
  1. Qiang Huang
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  2. Xiaomei Wu
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Corresponding author

Correspondence to Xiaomei Wu.

Additional information

This work was supported by the Science Foundation of Zhejiang Education Department (No. Y201738640) and the National Natural Science Foundation of China (Nos. 11801518, 11671362).

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Huang, Q., Wu, X. Boundedness of Iterated Spherical Average on α-Modulation Spaces. Chin. Ann. Math. Ser. B 42, 721–736 (2021). https://doi.org/10.1007/s11401-021-0287-0

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  • DOI: https://doi.org/10.1007/s11401-021-0287-0

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