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

A. M. Stokolos

ArticleOriginal scientific text

Title

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

Authors ¹

Affiliations

Institute of Mathematics, Economics and Mechanics, Odessa State University, Petra Velikogo 2, 270000 Odessa, Ukraine

Abstract

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^{ω}_{1} (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.

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Title

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

Affiliations

Abstract

Bibliography