Elementary construction of Hölder functions such that the Kurzweil-Stieltjes integral does not exist
Czechoslovak Mathematical Journal (2025)
- Issue: 1, page 345-356
- ISSN: 0011-4642
Access Full Article
top
Abstract
topHow to cite
topRmoutil, Martin. "Elementary construction of Hölder functions such that the Kurzweil-Stieltjes integral does not exist." Czechoslovak Mathematical Journal (2025): 345-356. <http://eudml.org/doc/299923>.
@article{Rmoutil2025,
abstract = {For any $\alpha , \beta >0$ with $\alpha +\beta <1$ we provide a simple construction of an $\alpha $-Hölde function $f\colon [0,1]\rightarrow \{\mathbb \{R\}\}$ and a $\beta $-Hölder function $g\colon [0,1]\rightarrow \{\mathbb \{R\}\}$ such that the integral $\int _0^1 f \{\rm d\} g$ fails to exist even in the Kurzweil-Stieltjes sense.},
author = {Rmoutil, Martin},
journal = {Czechoslovak Mathematical Journal},
keywords = {Kurzweil-Stieltjes integral; Hölder function; counterexample},
language = {eng},
number = {1},
pages = {345-356},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Elementary construction of Hölder functions such that the Kurzweil-Stieltjes integral does not exist},
url = {http://eudml.org/doc/299923},
year = {2025},
}
TY - JOUR
AU - Rmoutil, Martin
TI - Elementary construction of Hölder functions such that the Kurzweil-Stieltjes integral does not exist
JO - Czechoslovak Mathematical Journal
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 345
EP - 356
AB - For any $\alpha , \beta >0$ with $\alpha +\beta <1$ we provide a simple construction of an $\alpha $-Hölde function $f\colon [0,1]\rightarrow {\mathbb {R}}$ and a $\beta $-Hölder function $g\colon [0,1]\rightarrow {\mathbb {R}}$ such that the integral $\int _0^1 f {\rm d} g$ fails to exist even in the Kurzweil-Stieltjes sense.
LA - eng
KW - Kurzweil-Stieltjes integral; Hölder function; counterexample
UR - http://eudml.org/doc/299923
ER -
References
top- Dudley, R. M., Norvaiša, R., 10.1007/BFb0100744, Lecture Notes in Mathematics 1703. Springer, Berlin (1999). (1999) Zbl0973.46033MR1705318DOI10.1007/BFb0100744
- Dudley, R. M., Norvaiša, R., 10.1007/978-1-4419-6950-7, Springer Monographs in Mathematics. Springer, New York (2011). (2011) Zbl1218.46003MR2732563DOI10.1007/978-1-4419-6950-7
- Hardy, G. H., 10.1090/S0002-9947-1916-1501044-1, Trans. Am. Math. Soc. 17 (1916), 301-325 9999JFM99999 46.0401.03. (1916) MR1501044DOI10.1090/S0002-9947-1916-1501044-1
- Lacina, F., Stochastic Integrals: Master's Thesis, Charles University, Prague (2016), Available at http://hdl.handle.net/20.500.11956/75283. (2016)
- Leśniewicz, R., Orlicz, W., 10.4064/sm-45-1-71-109, Stud. Math. 45 (1973), 71-109. (1973) Zbl0218.26007MR346509DOI10.4064/sm-45-1-71-109
- Monteiro, G. A., Slavík, A., Tvrdý, M., 10.1142/9432, Series in Real Analysis 15. World Scientific, Hackensack (2019). (2019) Zbl1437.28001MR3839599DOI10.1142/9432
- Young, L. C., 10.1007/BF02401743, Acta Math. 67 (1936), 251-282. (1936) Zbl0016.10404MR1555421DOI10.1007/BF02401743
- Zygmund, A., 10.1017/CBO9781316036587, Cambridge Mathematical Library. Cambridge University Press, Cambridge (2002). (2002) Zbl1084.42003MR1963498DOI10.1017/CBO9781316036587
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.