Bessel capacities and rectangular differentiation in Besov spaces

We consider the differentiation of integrals of functions in Besov spaces with respect to the basis of arbitrarily oriented rectangular parallelepipeds in Rn. We study almost everywhere convergence with respect to Bessel capacities. These outer measures are more sensitive than n-dimensional Lebesgue measure, and therefore we improve the positive results in [H. Aimar, L. Forzani, V. Naibo, Rectangular differentiation of integrals of Besov functions, Math. Res. Lett. 9 (2–3) (2002) 173–189]. © 2005 Elsevier Inc. All rights reserved.