On the (1/2,+)-caloric capacity of Cantor sets
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.
Keywords:
Fractional heat equation, singular integrals, Cantor set
Affiliations des auteurs :
Joan Hernández 1
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
@article{AFM_2024_49_1_a10,
author = {Joan Hern\'andez},
title = {On the (1/2,+)-caloric capacity of {Cantor} sets},
journal = {Annales Fennici Mathematici},
pages = {211{\textendash}239--211{\textendash}239},
year = {2024},
volume = {49},
number = {1},
doi = {10.54330/afm.144428},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.54330/afm.144428/}
}
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