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Besov capacity for a class of nonlocal hypoelliptic operators and its applications

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Abstract

In this paper, we introduce the Besov capacity associated with a class of nonlocal hypoelliptic operators in \({\mathbb {R}}^{N}.\) Some measure theories and geometric properties for this capacity are established. As applications we study quasicontinuous representatives in the Besov space and we also obtain some important inequalities involving the Besov capacity established in this paper.

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Acknowledgements

The authors are grateful to the anonymous referee for careful reading and valuable comments that helped to improve the paper. Y. Liu was supported by the National Natural Science Foundation of China (No. 11671031, No. 12271042) and Beijing Natural Science Foundation of China (No. 1232023).

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  1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China

    Nan Zhao & Yu Liu

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  1. Nan Zhao
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Correspondence to Yu Liu.

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Zhao, N., Liu, Y. Besov capacity for a class of nonlocal hypoelliptic operators and its applications. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 168 (2023). https://doi.org/10.1007/s13398-023-01499-3

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