Hostname: page-component-7479d7b7d-m9pkr Total loading time: 0 Render date: 2024-07-10T23:36:56.691Z Has data issue: false hasContentIssue false
  • English
  • Français

Characterisation of multipliers for the double Henstock integrals

Published online by Cambridge University Press:  17 April 2009

Lee Tuo-Yeong ,
Chew Tuan-Seng  and
Lee Peng-Yee
Lee Tuo-Yeong
Affiliation:
Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 0511
Chew Tuan-Seng
Affiliation:
Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 0511
Lee Peng-Yee
Affiliation:
Mathematics Division, National Institute of Education, Nanyang Technological University, Bukit Timah Rd, Singapore 1025
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we prove that fg is Henstock integrable on an interval in the Euclidean space for each Henstock integrable function f if and only if g is a function of essentially strongly bounded variation.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 3 , December 1996 , pp. 441 - 449
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Alexiewicz, A., ‘Linear functionals on Denjoy integrable functions’, Colloq. Math. 1 (1948), 289–293.CrossRefGoogle Scholar
[2]Henstock, R., Lectures on the theory of integration (World Scientific, 1988).CrossRefGoogle Scholar
[3]Henstock, R., The general theory of integration (Clarendon Press, Oxford, 1991).CrossRefGoogle Scholar
[4]Kurzweil, J., ‘On multiplication of Perron-integrable functions’, Czechoslovak Math J. 23 (1973), 542–566.CrossRefGoogle Scholar
[5]Yee, Lee Peng, Lanzhou lectures on Henstock integration (World Scientific, 1989).Google Scholar
[6]Yee, Lee Peng, ‘Measurability and the Henstock integral’, in Proc. International Math. Conf. (Kaohsiung 1994) (World Scientific, 1995), pp. 99–106.Google Scholar
[7]McLeod, R.M., The generalized Riemann integral, Carus Math Monographs 20 (Math. Assoc. America, Washington DC, 1980).CrossRefGoogle Scholar
[8]Mikusiński, P. and Ostaszewski, K., ‘The space of Henstock integrable functions II’, in New integrals, ( Bullen, P.S., Lee, P.Y., Mawhin, J.L., Muldowney, P. and Pfeffer, W.F., Editors), Lecture Notes in Math. 1419 (Springer-Verlag, Berlin, Heidelberg, New York, 1990), pp. 136–149.CrossRefGoogle Scholar
[9]Ostaszewski, K., ‘The space of Henstock integrable functions of two variables’, Internat. J. Math. Math. Sci. 1 (1988), 15–22.CrossRefGoogle Scholar
[10]Pfeffer, W.F., ‘A Riemann-type integration and the fundamental theorem of calculus’, Rend. Circ. Mat. Palermo 36 (1987), 482–506.CrossRefGoogle Scholar
[11]Sargent, W.L.C., ‘On the integrability of a product’, J. London Math. Soc. 23 (1948), 28–34.CrossRefGoogle Scholar
[12]Guoju, Ye and Yee, Lee Peng, ‘A version of Harnack extension for the Henstock integral’, J. Mathematical study Vol 28, 106–108.Google Scholar