An α-number characterization of Lp spaces on uniformly rectifiable sets

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Jonas Azzam
Damian Dąbrowski

We give a characterization of Lp(σ) for uniformly rectifiable measures σ using Tolsa’s α-numbers, by showing, for 1 < p < ∞ and f ∈ Lp(σ), that kfkLp(σ) ∼Z ∞0(αfσ(x, r) + |f|x,rασ(x, r))2drr12Lp(σ).

Paraules clau
quantitative rectifiability, uniformly rectifiable sets, α-numbers, Lp spaces

Article Details

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Azzam, Jonas; and Dąbrowski, Damian. “An α-number characterization of Lp spaces on uniformly rectifiable sets”. Publicacions Matemàtiques, vol.VOL 67, no. 2, pp. 819-50, https://raco.cat/index.php/PublicacionsMatematiques/article/view/418513.
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