Czechoslovak Mathematical Journal, Vol. 63, No. 1, pp. 1-38, 2013

Two convergence theorems for Henstock-Kurzweil integrals and their applications to multiple trigonometric series

Tuo-Yeong Lee

Tuo-Yeong Lee, Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Republic of Singapore, e-mail:

Abstract: We establish two new norm convergence theorems for Henstock-Kurzweil integrals. In particular, we provide a unified approach for extending several results of R. P. Boas and P. Heywood from one-dimensional to multidimensional trigonometric series.

Keywords: Henstock-Kurzweil integral, regularly convergent multiple series

Classification (MSC 2010): 42B05, 26A39

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