Rectangular differentiation of integrals of Besov functions

AIMAR HUGO; FORZANI LILIANA; NAIBO VIRGINIA

MATHEMATICAL RESEARCH LETTERS

INT PRESS BOSTON, INC

Año: 2002 vol. 9 p. 173 - 189

1073-2780

We study the differentiation of integrals of functions in the Besovspaces B^(α,1)_p (R^n), α > 0, 1 ≤ p < ∞, with respect to the basis of arbitrarilyoriented rectangular parallelepipeds in R^n. We show that positive results hold if α ≥( n−1)/p and we give counterexamples for the case 0 < α < n/p −1. Similar resultshold for B^(α,q)_p (R^n), q > 1. For more general bases we can also prove negative resultsfor n/p − 1 ≤ α < (n−1)/p .