Electron. J. Diff. Equ., Vol. 2015 (2015), No. 44, pp. 1-7.

Integration by parts for the $L^r$ Henstock-Kurzweil integral

Paul Musial, Francesco Tulone

Abstract:
Musial and Sagher [4] described a Henstock-Kurzweil type integral that integrates $L^r$-derivatives. In this article, we develop a product rule for the $L^r$-derivative and then an integration by parts formula.

Submitted December 8, 2014. Published February 16, 2015.
Math Subject Classifications: 26A39.
Key Words: Henstock-Kurzweil; integration by parts.

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Paul Musial
Department of Mathematics and Computer Science
Chicago State University
9501 South King Drive
Chicago, Illinois 60628, USA
email: pmusial@csu.edu
Francesco Tulone
Department of Mathematics and Computer Science
University of Palermo
Via Archirafi, 34
90132 Palermo, Italy
email: francesco.tulone@unipa.it

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