Displaying similar documents to “A general result on the equivalence between derivation of integrals and weak inequalities for the Hardy-Littlewood maximal operator”

On differentiation of integrals with respect to bases of convex sets.

A. Stokolos (1996)

Studia Mathematica

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Differentiation of integrals of functions from the class L i p ( 1 , 1 ) ( I 2 ) with respect to the basis of convex sets is established. An estimate of the rate of differentiation is given. It is also shown that there exist functions in L i p ( 1 , 1 ) ( I N ) , N ≥ 3, and H 1 ω ( I 2 ) with ω(δ)/δ → ∞ as δ → +0 whose integrals are not differentiated with respect to the bases of convex sets in the corresponding dimension.