CC BY 4.0 UnportedFriz, Peter K.Tran, Huy2022-06-222022-06-222017https://oa.tib.eu/renate/handle/123456789/9111https://doi.org/10.34657/8149We revisit regularity of SLE trace, for all κ≠8, and establish Besov regularity under the usual half-space capacity parametrization. With an embedding theorem of Garsia–Rodemich–Rumsey type, we obtain finite moments (and hence almost surely) optimal variation regularity with index min(1+κ/8,2), improving on previous works of Werness, and also (optimal) Hölder regularity à la Johansson Viklund and Lawler.enghttps://creativecommons.org/licenses/by/4.0/510Article