Geodesic
On the (1/2,+)-caloric capacity of Cantor sets
Joan Hernández1
1 Universitat Autònoma de Barcelona, Departament de Matemàtiques
Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 211–239.

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In the present paper we characterize the (1/2,+)-caloric capacity (associated with the 1/2-fractional heat equation) of the usual corner-like Cantor set of $\mathbb{R}^{n+1}$. The results obtained for the latter are analogous to those found for Newtonian capacity. Moreover, we also characterize the BMO and Lip$_\alpha$ variants ($0<\alpha<1$) of the 1/2-caloric capacity in terms of the Hausdorff contents $H^n_\infty$ and $H^{n+\alpha}_\infty$ respectively.
DOI : 10.54330/afm.144428
Keywords: Fractional heat equation, singular integrals, Cantor set

Joan Hernández 1

1 Universitat Autònoma de Barcelona, Departament de Matemàtiques 
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Joan Hernández. On the (1/2,+)-caloric capacity of Cantor sets. Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 211–239. doi : 10.54330/afm.144428. http://geodesic.mathdoc.fr/articles/10.54330/afm.144428/

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