The Henstock-Kurzweil approach to Young integrals with integrators in BV φ

Boonpogkrong Varayu; Tuan-Seng Chew

Mathematica Bohemica (2006)

  • Volume: 131, Issue: 3, page 233-260
  • ISSN: 0862-7959

Abstract

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In 1938, L. C. Young proved that the Moore-Pollard-Stieltjes integral ∫ a b f d g exists if f ∈ B V φ [ a , b ] , g ∈ B V ψ [ a , b ] and ∑ n = 1 ∞ φ - 1 ( 1 / n ) ψ - 1 ( 1 / n ) < ∞ . In this note we use the Henstock-Kurzweil approach to handle the above integral defined by Young.

How to cite

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Varayu, Boonpogkrong, and Chew, Tuan-Seng. "The Henstock-Kurzweil approach to Young integrals with integrators in ${\rm BV}_\phi $." Mathematica Bohemica 131.3 (2006): 233-260. <http://eudml.org/doc/249918>.

@article{Varayu2006,
abstract = {In 1938, L. C. Young proved that the Moore-Pollard-Stieltjes integral $\int _a^bf\mathrm \{d\}g$ exists if $f\in \mathop \{\{\mathrm \{B\}V\}\}_\phi [a,b]$, $g\in \mathop \{\{\mathrm \{B\}V\}\}_\psi [a,b]$ and $\sum _\{n=1\}^\infty \phi ^\{-1\}(\{1\}/\{n\})\psi ^\{-1\} (\{1\}/\{n\})<\infty $. In this note we use the Henstock-Kurzweil approach to handle the above integral defined by Young.},
author = {Varayu, Boonpogkrong, Chew, Tuan-Seng},
journal = {Mathematica Bohemica},
keywords = {Henstock integral; Stieltjes integral; Young integral; $\phi $-variation; Henstock integral; Stieltjes integral; Young integral; -variation},
language = {eng},
number = {3},
pages = {233-260},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The Henstock-Kurzweil approach to Young integrals with integrators in $\{\rm BV\}_\phi $},
url = {http://eudml.org/doc/249918},
volume = {131},
year = {2006},
}

TY - JOUR
AU - Varayu, Boonpogkrong
AU - Chew, Tuan-Seng
TI - The Henstock-Kurzweil approach to Young integrals with integrators in ${\rm BV}_\phi $
JO - Mathematica Bohemica
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 131
IS - 3
SP - 233
EP - 260
AB - In 1938, L. C. Young proved that the Moore-Pollard-Stieltjes integral $\int _a^bf\mathrm {d}g$ exists if $f\in \mathop {{\mathrm {B}V}}_\phi [a,b]$, $g\in \mathop {{\mathrm {B}V}}_\psi [a,b]$ and $\sum _{n=1}^\infty \phi ^{-1}({1}/{n})\psi ^{-1} ({1}/{n})<\infty $. In this note we use the Henstock-Kurzweil approach to handle the above integral defined by Young.
LA - eng
KW - Henstock integral; Stieltjes integral; Young integral; $\phi $-variation; Henstock integral; Stieltjes integral; Young integral; -variation
UR - http://eudml.org/doc/249918
ER -

References

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  10. A note on integration by parts for abstract Perron-Stieltjes integrals, Math. Bohem. 126 (2001), 613–629. (2001) Zbl0980.26005MR1970264
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