Rectangular differentiation of integrals of Besov functions - Aimar, Hugo Alejandro (2002)
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 α≥ \frac{n-1}{p} and we give counterexamples for the case 0<α 1: For more general bases we can also prove negative results n/p-1=<α<(n-1)/p.