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Besov and Triebel-Lizorkin Capacity in Metric Spaces

  • Nijjwal Karak EMAIL logo and Debarati Mondal
Published/Copyright: August 4, 2023
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ABSTRACT

We prove a lower bound estimate for Hajłasz-Besov capacity in metric spaces in terms of Netrusov-Hausdorff content. We also prove a similar estimate for Hajłasz-Triebel-Lizorkin capacity in terms of Hausdoroff content. These results are improvements of the earlier results obtained by Nuutinen in 2016 and the first author in 2020.

2020 Mathematics Subject Classification: Primary 31E05; 31B15

(Communicated by L’ubica Holá)


Funding statement: N. K. would like to thank BITS Pilani (BITS/GAU/RIG/2020/H0749) and DST-SERB (SRG/2021/000118), and D. M. would like to thank BITS Pilani (ID no. 2020PHXF0038H) for the financial support.

Funding statement: The authors are also thankful to Prof. Tord Sjödin for asking the question answered in this paper.

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Received: 2022-06-11
Accepted: 2022-11-12
Published Online: 2023-08-04

© 2023 Mathematical Institute Slovak Academy of Sciences

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