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The Denjoy extension of the Riemann and McShane integrals

Jae Myung Park (2000)

Czechoslovak Mathematical Journal

In this paper we study the Denjoy-Riemann and Denjoy-McShane integrals of functions mapping an interval a , b into a Banach space X . It is shown that a Denjoy-Bochner integrable function on a , b is Denjoy-Riemann integrable on a , b , that a Denjoy-Riemann integrable function on a , b is Denjoy-McShane integrable on a , b and that a Denjoy-McShane integrable function on a , b is Denjoy-Pettis integrable on a , b . In addition, it is shown that for spaces that do not contain a copy of c 0 , a measurable Denjoy-McShane integrable...

The dual of the space of functions of bounded variation

Khaing Khaing Aye, Peng Yee Lee (2006)

Mathematica Bohemica

In the paper, we show that the space of functions of bounded variation and the space of regulated functions are, in some sense, the dual space of each other, involving the Henstock-Kurzweil-Stieltjes integral.

The Fourier transform in Lebesgue spaces

Erik Talvila (2025)

Czechoslovak Mathematical Journal

For each f L p ( ) ( 1 p < ) it is shown that the Fourier transform is the distributional derivative of a Hölder continuous function. For each p , a norm is defined so that the space of Fourier transforms is isometrically isomorphic to L p ( ) . There is an exchange theorem and inversion in norm.

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