Rectangular differentiation of integrals of Besov functions

Abstract

We study the dierentiation of integrals of functions in the Besov spaces B;1p (Rn); > 0; 1 p < 1; with respect to the basis of arbitrarily oriented rectangular parallelepipeds in Rn: We show that positive results hold if \alpha\geq \frac{n-1}{p} and we give counterexamples for the case 0<\alpha 1: For more general bases we can also prove negative results n/p-1=<\alpha<(n-1)/p.