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Sobolev Regularity of Maximal Operators on Infinite Connected Graphs

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Abstract

Let G be an infinite connected graph. We study the Sobolev regularity for the Hardy–Littlewood maximal operator and its fractional variants on G. Under certain geometric conditions on G, the endpoint Sobolev regularity properties for the above maximal operators are established. In addition, we introduce Hajłasz–Sobolev spaces on G and show that the above operators are bounded on the above function spaces.

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Acknowledgements

The authors want to express their sincerely thanks to the referee for his or her valuable remarks and suggestions, which 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

    Feng Liu & Xiao Zhang

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

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

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Liu, F., Zhang, X. Sobolev Regularity of Maximal Operators on Infinite Connected Graphs. Mediterr. J. Math. 18, 105 (2021). https://doi.org/10.1007/s00009-021-01759-9

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  • DOI: https://doi.org/10.1007/s00009-021-01759-9

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