Some characterizations of the primitive of strong Henstock-Kurzweil integrable functions

Guoju Ye

Mathematica Bohemica (2006)

  • Volume: 131, Issue: 3, page 279-290
  • ISSN: 0862-7959

Abstract

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In this paper we give some complete characterizations of the primitive of strongly Henstock-Kurzweil integrable functions which are defined on ℝ m with values in a Banach space.

How to cite

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Ye, Guoju. "Some characterizations of the primitive of strong Henstock-Kurzweil integrable functions." Mathematica Bohemica 131.3 (2006): 279-290. <http://eudml.org/doc/249916>.

@article{Ye2006,
abstract = {In this paper we give some complete characterizations of the primitive of strongly Henstock-Kurzweil integrable functions which are defined on $\mathbb \{R\}^m$ with values in a Banach space.},
author = {Ye, Guoju},
journal = {Mathematica Bohemica},
keywords = {strong Henstock-Kurzweil integral; inner variation; $\mathop \{\text\{SL\}\}$ condition; inner variation; condition},
language = {eng},
number = {3},
pages = {279-290},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some characterizations of the primitive of strong Henstock-Kurzweil integrable functions},
url = {http://eudml.org/doc/249916},
volume = {131},
year = {2006},
}

TY - JOUR
AU - Ye, Guoju
TI - Some characterizations of the primitive of strong Henstock-Kurzweil integrable functions
JO - Mathematica Bohemica
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 131
IS - 3
SP - 279
EP - 290
AB - In this paper we give some complete characterizations of the primitive of strongly Henstock-Kurzweil integrable functions which are defined on $\mathbb {R}^m$ with values in a Banach space.
LA - eng
KW - strong Henstock-Kurzweil integral; inner variation; $\mathop {\text{SL}}$ condition; inner variation; condition
UR - http://eudml.org/doc/249916
ER -

References

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  1. Topics in Banach space integration, World Scientific, Singapore, 2005. (2005) MR2167754
  2. Some full characterizations of strong McShane integral functions, Math. Bohem. 129 (2004), 305–312. (2004) MR2092716
  3. On Henstock’s inner variation and strong derivatives, Real Anal. Exch. 24 (2001/2002), 725–733. (2001/2002) MR1923161
  4. Lanzhou Lectures on Henstock Integration, World Scientific, Singapore, 1989. (1989) Zbl0699.26004MR1050957
  5. The general theory of integration, Oxford University Press, Oxford, 1991. (1991) Zbl0745.26006MR1134656
  6. The primitives of Henstock integrable functions in Euclidean space, Bull. Lond. Math. Society, 31 (1999), 137–180. (1999) MR1664188
  7. Banach-valued HL multiple integral, Research Report No. 788, National University of Singapore 788 (2002), 1–20. (2002) 
  8. Controlled convergence theorem for strong variational Banach-valued multiple integrals, Real Anal. Exch. 28 (2002/2003), 579–591. (2002/2003) MR2010339

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