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

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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.

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  1. Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore, 637616, Republic of Singapore

    Tuo-Yeong Lee

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Lee, TY. Two convergence theorems for Henstock-Kurzweil integrals and their applications to multiple trigonometric series. Czech Math J 63, 1–38 (2013). https://doi.org/10.1007/s10587-013-0001-9

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  • DOI: https://doi.org/10.1007/s10587-013-0001-9

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