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A full characterization of multipliers for the strong ρ -integral in the euclidean space

Lee Tuo-Yeong (2004)

Czechoslovak Mathematical Journal

We study a generalization of the classical Henstock-Kurzweil integral, known as the strong ρ -integral, introduced by Jarník and Kurzweil. Let ( 𝒮 ρ ( E ) , · ) be the space of all strongly ρ -integrable functions on a multidimensional compact interval E , equipped with the Alexiewicz norm · . We show that each element in the dual space of ( 𝒮 ρ ( E ) , · ) can be represented as a strong ρ -integral. Consequently, we prove that f g is strongly ρ -integrable on E for each strongly ρ -integrable function f if and only if g is almost everywhere...

A remark on the div-curl lemma

Pierre Gilles Lemarié-Rieusset (2012)

Studia Mathematica

We prove the div-curl lemma for a general class of function spaces, stable under the action of Calderón-Zygmund operators. The proof is based on a variant of the renormalization of the product introduced by S. Dobyinsky, and on the use of divergence-free wavelet bases.

A topology on inequalities.

D'Aristotile, Anna Maria, Fiorenza, Alberto (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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