TY - JOUR
T1 - Hausdorff measure and decay rate of Riesz capacity
AU - Fan, Qiuling
AU - Laugesen, Richard S.
N1 - Laugesen was supported by awards from the Simons Foundation (grant number 964018) and the National Science Foundation (grant number 2246537). Fan was supported by the National Science Foundation award to Laugesen (grant number 2246537).
PY - 2025/10/15
Y1 - 2025/10/15
N2 - The decay rate of Riesz capacity as the exponent increases to the dimension of the set is shown to yield Hausdorff measure. The result applies to strongly rectifiable sets, and so in particular to submanifolds of Euclidean space. For strictly self-similar fractals, a one-sided decay estimate is found. Along the way, a purely measure theoretic proof is given for subadditivity of the reciprocal of Riesz energy.
AB - The decay rate of Riesz capacity as the exponent increases to the dimension of the set is shown to yield Hausdorff measure. The result applies to strongly rectifiable sets, and so in particular to submanifolds of Euclidean space. For strictly self-similar fractals, a one-sided decay estimate is found. Along the way, a purely measure theoretic proof is given for subadditivity of the reciprocal of Riesz energy.
KW - Strictly self-similar
KW - Strongly rectifiable
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U2 - 10.1016/j.jmaa.2025.129625
DO - 10.1016/j.jmaa.2025.129625
M3 - Article
AN - SCOPUS:105004290408
SN - 0022-247X
VL - 550
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
M1 - 129625
ER -