A multidimensional integration by parts formula for the Henstock-Kurzweil integral

Tuo-Yeong Lee

Displaying similar documents to “A multidimensional integration by parts formula for the Henstock-Kurzweil integral”

Multipliers for generalized Riemann integrals in the real line

Tuo-Yeong Lee (2006)

Mathematica Bohemica

Similarity:

We use an elementary method to prove that each $B V$ function is a multiplier for the $C$ -integral.

Henstock-Kurzweil and McShane product integration; descriptive definitions

Antonín Slavík, Štefan Schwabik (2008)

Czechoslovak Mathematical Journal

Similarity:

The Henstock-Kurzweil and McShane product integrals generalize the notion of the Riemann product integral. We study properties of the corresponding indefinite integrals (i.e. product integrals considered as functions of the upper bound of integration). It is shown that the indefinite McShane product integral of a matrix-valued function $A$ is absolutely continuous. As a consequence we obtain that the McShane product integral of $A$ over $[a, b]$ exists and is invertible if and only if $A$ is Bochner...

Bounded linear functionals on the space of Henstock-Kurzweil integrable functions

Tuo-Yeong Lee (2009)

Czechoslovak Mathematical Journal

Similarity:

Applying a simple integration by parts formula for the Henstock-Kurzweil integral, we obtain a simple proof of the Riesz representation theorem for the space of Henstock-Kurzweil integrable functions. Consequently, we give sufficient conditions for the existence and equality of two iterated Henstock-Kurzweil integrals.