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On the spherical maximal function on finite graphs

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

This paper is devoted to studying the mapping properties for the spherical maximal operator \({\mathbf {S}}_G\) defined on finite connected graphs G. Some operator norms of \({\mathbf {S}}_G\) on the \(\ell ^p(G)\), \(\ell ^{p,\infty }(G)\) and the spaces of bounded p-variation functions defined on G are investigated. Particularly, as some special examples of finite connected graphs, the complete graph \(K_n\) and star graph \(S_n\) are discussed.

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Acknowledgements

The authors would like to express their sincerely thanks to the referee for his or her valuable remarks and suggestions, which help us to improve partial results of this paper and made this paper more readable.

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  1. College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, 266590, Shandong, People’s Republic of China

    Xiao Zhang & Feng Liu

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  1. Xiao Zhang
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  2. Feng Liu
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Correspondence to Feng Liu.

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The work was supported partly by the NNSF of China (Grant No. 11701333).

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Zhang, X., Liu, F. On the spherical maximal function on finite graphs. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 115, 186 (2021). https://doi.org/10.1007/s13398-021-01127-y

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