International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 497-501
A property of integral transformations
Department of Mathematics, University of Wisconsin-Oshkosh, Oshkosh 54901, Wisconsin, USA
Received 11 April 1984
Copyright © 1984 Yu Chuen Wei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The main result of this paper is the result that the collection of all integral transformations of the form for all , where is defined on and defined on has no identity transformation on , where is the space of functions that are Lebesgue integrable on with norm . That is to say, there is no defined on such that for every , for almost all . In addition, this paper gives a theorem that is an improvement of a theorem that is proved by J. B. Tatchell (1953) and Sunonchi and Tsuchikura (1952).