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

• Autorzy: A. M. Stokolos
• Języki publikacji: EN

Abstrakty

EN

Differentiation of integrals of functions from the class $Lip(1,1)(I^2)$ 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 $Lip(1,1)(I^N)$, 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.

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory
• 28A15: Abstract differentiation theory, differentiation of set functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 119
• Numer: 2
• Strony: 99-108

Daty

wydano

1996

otrzymano

1993-03-10

poprawiono

1996-03-10

poprawiono

1996-03-18

Twórcy

autor

A. M. Stokolos

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

Bibliografia

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• [3] M. de Guzmán, Real Variable Methods in Fourier Analysis, North-Holland Math. Stud. 46, Amsterdam, 1981.
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• [8] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970.
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