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Volume 36, Issue 4
Lipschitz Invariance of Critical Exponents on Besov Spaces

Qingsong Gu & Hui Rao

DOI: 10.4208/ata.OA-SU5

Anal. Theory Appl., 36 (2020), pp. 457-467.

Published online: 2020-12

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper we prove that the critical exponents of Besov spaces on a compact set possessing an Ahlfors regular measure is an invariant under Lipschitz transforms. Under mild conditions, the critical exponent of Besov spaces of certain self-similar sets coincides with the walk dimension, which plays an important role in the analysis on fractals. As an application, we show examples having different critical exponents are not Lipschitz equivalent.

  • Keywords

Lipschitz invariant, Besov space, critical exponents, walk dimension, heat kernel.

  • AMS Subject Headings

35K08, 28A80, 35J08, 46E35, 47D07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-36-457, author = {Gu , Qingsong and Rao , Hui}, title = {Lipschitz Invariance of Critical Exponents on Besov Spaces}, journal = {Analysis in Theory and Applications}, year = {2020}, volume = {36}, number = {4}, pages = {457--467}, abstract = {

In this paper we prove that the critical exponents of Besov spaces on a compact set possessing an Ahlfors regular measure is an invariant under Lipschitz transforms. Under mild conditions, the critical exponent of Besov spaces of certain self-similar sets coincides with the walk dimension, which plays an important role in the analysis on fractals. As an application, we show examples having different critical exponents are not Lipschitz equivalent.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-SU5}, url = {http://global-sci.org/intro/article_detail/ata/18463.html} }
TY - JOUR T1 - Lipschitz Invariance of Critical Exponents on Besov Spaces AU - Gu , Qingsong AU - Rao , Hui JO - Analysis in Theory and Applications VL - 4 SP - 457 EP - 467 PY - 2020 DA - 2020/12 SN - 36 DO - http://doi.org/10.4208/ata.OA-SU5 UR - https://global-sci.org/intro/article_detail/ata/18463.html KW - Lipschitz invariant, Besov space, critical exponents, walk dimension, heat kernel. AB -

In this paper we prove that the critical exponents of Besov spaces on a compact set possessing an Ahlfors regular measure is an invariant under Lipschitz transforms. Under mild conditions, the critical exponent of Besov spaces of certain self-similar sets coincides with the walk dimension, which plays an important role in the analysis on fractals. As an application, we show examples having different critical exponents are not Lipschitz equivalent.

Gu , Qingsong and Rao , Hui. (2020). Lipschitz Invariance of Critical Exponents on Besov Spaces. Analysis in Theory and Applications. 36 (4). 457-467. doi:10.4208/ata.OA-SU5
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