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

Tuo-Yeong Lee

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 1, page 1-38
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Lee, Tuo-Yeong. "Two convergence theorems for Henstock-Kurzweil integrals and their applications to multiple trigonometric series." Czechoslovak Mathematical Journal 63.1 (2013): 1-38. <http://eudml.org/doc/252543>.

@article{Lee2013,
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.},
author = {Lee, Tuo-Yeong},
journal = {Czechoslovak Mathematical Journal},
keywords = {Henstock-Kurzweil integral; regularly convergent multiple series; multiple Henstock-Kurzweil integral; regularly convergent multiple series; multiple trigonometric series},
language = {eng},
number = {1},
pages = {1-38},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Two convergence theorems for Henstock-Kurzweil integrals and their applications to multiple trigonometric series},
url = {http://eudml.org/doc/252543},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Lee, Tuo-Yeong
TI - Two convergence theorems for Henstock-Kurzweil integrals and their applications to multiple trigonometric series
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 1
SP - 1
EP - 38
AB - 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.
LA - eng
KW - Henstock-Kurzweil integral; regularly convergent multiple series; multiple Henstock-Kurzweil integral; regularly convergent multiple series; multiple trigonometric series
UR - http://eudml.org/doc/252543
ER -

References

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