Title:
|
Adjoint classes of functions in the $H\sb 1$ sense (English) |
Author:
|
Sworowski, Piotr |
Language:
|
English |
Journal:
|
Czechoslovak Mathematical Journal |
ISSN:
|
0011-4642 (print) |
ISSN:
|
1572-9141 (online) |
Volume:
|
57 |
Issue:
|
2 |
Year:
|
2007 |
Pages:
|
505-522 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
Using the concept of the $ {\mathrm H}_1$-integral, we consider a similarly defined Stieltjes integral. We prove a Riemann-Lebesgue type theorem for this integral and give examples of adjoint classes of functions. (English) |
Keyword:
|
Stieltjes integral |
Keyword:
|
Kurzweil integral |
Keyword:
|
Henstock integral |
Keyword:
|
${\mathrm H}_1$-integral |
Keyword:
|
Riemann-Lebesgue theorem |
Keyword:
|
variational measure |
Keyword:
|
adjoint classes |
MSC:
|
26A39 |
idZBL:
|
Zbl 1174.26310 |
idMR:
|
MR2337612 |
. |
Date available:
|
2009-09-24T11:47:20Z |
Last updated:
|
2020-07-03 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128187 |
. |
Reference:
|
[1] H. Chen: A pair of adjoint classes of Riemann-Stieltjes integrable functions.Real Anal. Exch. 23 (1998), 235–240. MR 1609806 |
Reference:
|
[2] H. Chen: Adjoint classes of generalized Stieltjes integrable functions.Real Anal. Exch. 24 (1999), 139–148. MR 1691741 |
Reference:
|
[3] H. Chen: Adjoint classes of Lebesgue-Stieltjes integrable functions.Real Anal. Exch. 26 (2001), 421–427. Zbl 1023.26007, MR 1825521 |
Reference:
|
[4] I. J. L. Garces, P. Y. Lee: Cauchy and Harnack extensions for the $H_1$-integral.Matimyás Mat. 21 (1998), 28–34. MR 1710941 |
Reference:
|
[5] I. J. L. Garces, P. Y. Lee: Convergence theorems for the $H_1$-integral.Taiwanese J. Math. 4 (2000), 439–445. MR 1779108, 10.11650/twjm/1500407260 |
Reference:
|
[6] I. J. L. Garces, P. Y. Lee, and D. Zhao: Moore-Smith limits and the Henstock integral.Real Anal. Exch. 24 (1999), 447–455. MR 1691764 |
Reference:
|
[7] A. Maliszewski, P. Sworowski: Uniform convergence theorem for the $H_1$-integral revisited.Taiwanese J. Math. 7 (2003), 503–505. MR 1998771, 10.11650/twjm/1500558401 |
Reference:
|
[8] A. Maliszewski, P. Sworowski: A characterization of $H_1$-integrable functions.Real Anal. Exch. 28 (2003), 93–104. MR 1973971, 10.14321/realanalexch.28.1.0093 |
Reference:
|
[9] K. A. Ross: Another approach to Riemann-Stieltjes integrals.Am. Math. Mon. 87 (1980), 660–662. Zbl 0446.26005, MR 0600928, 10.2307/2320958 |
Reference:
|
[10] S. Saks: Theory of the Integral.G. E. Stechert, New York, 1937. Zbl 0017.30004 |
Reference:
|
[11] Š. Schwabik: On the relation between Young’s and Kurzweil’s concept of Stieltjes integral.Cas. Pest. Mat. 98 (1973), 237–251. Zbl 0266.26006, MR 0322113 |
Reference:
|
[12] P. Sworowski: On $H_1$-integrable functions.Real Anal. Exch. 27 (2002), 275–286. Zbl 1015.26017, MR 1887858 |
Reference:
|
[13] P. Sworowski: Some comments on the $H_1$-integral.Real Anal. Exch. 29 (2004), 789–797. Zbl 1078.26008, MR 2083813 |
Reference:
|
[14] P. Sworowski: Adjoint classes for generalized Riemann-Stieltjes integrals. 27th Summer Symposium Conference Reports, Opava 2003.Real Anal. Exch. (2003), 41–45. |
Reference:
|
[15] B. S. Thomson: Real Functions. Lecture Notes in Mathematics, Vol. 1170.Springer-Verlag, Berlin, 1985. MR 0818744 |
. |