On Kurzweil-Stieltjes equiintegrability and generalized BV functions

Giselle A. Monteiro

Mathematica Bohemica (2019)

  • Volume: 144, Issue: 4, page 423-436
  • ISSN: 0862-7959

Abstract

top
We present sufficient conditions ensuring Kurzweil-Stieltjes equiintegrability in the case when integrators belong to the class of functions of generalized bounded variation.

How to cite

top

Monteiro, Giselle A.. "On Kurzweil-Stieltjes equiintegrability and generalized BV functions." Mathematica Bohemica 144.4 (2019): 423-436. <http://eudml.org/doc/294759>.

@article{Monteiro2019,
abstract = {We present sufficient conditions ensuring Kurzweil-Stieltjes equiintegrability in the case when integrators belong to the class of functions of generalized bounded variation.},
author = {Monteiro, Giselle A.},
journal = {Mathematica Bohemica},
keywords = {Kurzweil-Stieltjes integral; generalized bounded variation; variational measure; Stieltjes derivative},
language = {eng},
number = {4},
pages = {423-436},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On Kurzweil-Stieltjes equiintegrability and generalized BV functions},
url = {http://eudml.org/doc/294759},
volume = {144},
year = {2019},
}

TY - JOUR
AU - Monteiro, Giselle A.
TI - On Kurzweil-Stieltjes equiintegrability and generalized BV functions
JO - Mathematica Bohemica
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 144
IS - 4
SP - 423
EP - 436
AB - We present sufficient conditions ensuring Kurzweil-Stieltjes equiintegrability in the case when integrators belong to the class of functions of generalized bounded variation.
LA - eng
KW - Kurzweil-Stieltjes integral; generalized bounded variation; variational measure; Stieltjes derivative
UR - http://eudml.org/doc/294759
ER -

References

top
  1. Bongiorno, B., Piazza, L. Di, 10.2307/44152212, Real Anal. Exch. 17 (1991-92), 339-361. (1991) Zbl0758.26006MR1147373DOI10.2307/44152212
  2. Bongiorno, B., Piazza, L. Di, Skvortsov, V., 10.2307/44152676, Real Anal. Exch. 21 (1995-96), 656-663. (1995) Zbl0879.26026MR1407278DOI10.2307/44152676
  3. Faure, C.-A., 10.2307/44152834, Real Anal. Exch. 23 (1998-99), 113-124. (1998) Zbl0944.26014MR1609775DOI10.2307/44152834
  4. Fraňková, D., Regulated functions, Math. Bohem. 116 (1991), 20-59. (1991) Zbl0724.26009MR1100424
  5. Frigon, M., Pouso, R. L., 10.1515/anona-2015-0158, Adv. Nonlinear Anal. 6 (2017), 13-36. (2017) Zbl1361.34010MR3604936DOI10.1515/anona-2015-0158
  6. Gordon, R. A., 10.2307/44152048, Real Anal. Exch. 15 (1989-90), 724-728. (1989) Zbl0708.26005MR1059433DOI10.2307/44152048
  7. Gordon, R. A., 10.1090/gsm/004, Graduate Studies in Mathematics 4. AMS, Providence (1994). (1994) Zbl0807.26004MR1288751DOI10.1090/gsm/004
  8. Hoffmann, H., Descriptive Characterisation of the Variational Henstock-Kurzweil-Stieltjes Integral and Applications, PhD thesis. Karlsruher Institue of Technology, Karlsruhe. Available at https://publikationen.bibliothek.kit.edu/1000046600 (2014). (2014) 
  9. Kurzweil, J., Jarník, J., 10.2307/44152200, Real Anal. Exch. 17 (1991-92), 110-139. (1991) Zbl0754.26003MR1147361DOI10.2307/44152200
  10. Lee, P. Y., 10.1142/0845, Series in Real Analysis 2. World Scientific, London (1989). (1989) Zbl0699.26004MR1050957DOI10.1142/0845
  11. Monteiro, G. A., Satco, B., 10.14232/ejqtde.2017.1.7, Electron. J. Qual. Theory Differ. Equ. 2017 (2017), Paper No. 7, 26 pages. (2017) Zbl06931238MR3606985DOI10.14232/ejqtde.2017.1.7
  12. Monteiro, G. A., Slavík, A., Tvrdý, M., 10.1142/9432, Series in Real Analysis 15. World Scientific, Hackensack (2019). (2019) Zbl06758513MR3839599DOI10.1142/9432
  13. Pouso, R. L., Rodríguez, A., 10.14321/realanalexch.40.2.0319, Real Anal. Exch. 40 (2015), 319-354. (2015) Zbl1384.26024MR3499768DOI10.14321/realanalexch.40.2.0319
  14. Saks, S., Theory of the Integral. With two additional notes by Stefan Banach, Monografie Matematyczne Tom. 7. G. E. Stechert & Co., New York (1937). (1937) Zbl0017.30004MR0167578
  15. Satco, B.-R., Measure integral inclusions with fast oscillating data, Electron. J. Differ. Equ. 2015 (2015), Paper No. 107, 13 pages. (2015) Zbl1314.45005MR3358479
  16. Schwabik, Š., 10.2478/s12175-009-0160-1, Math. Slovaca 59 (2009), 731-752. (2009) Zbl1212.26014MR2564330DOI10.2478/s12175-009-0160-1
  17. Schwabik, Š., 10.1007/s10587-010-0087-2, Czech. Math. J. 60 (2010), 961-981. (2010) Zbl1224.26030MR2738960DOI10.1007/s10587-010-0087-2
  18. Schwabik, Š., 10.1007/s10587-010-0088-1, Czech. Math. J. 60 (2010), 983-1005. (2010) Zbl1224.26031MR2738961DOI10.1007/s10587-010-0088-1
  19. Schwabik, Š., Vrkoč, I., 10.21136/MB.1996.126102, Math. Bohem. 121 (1996), 189-207. (1996) Zbl0863.26009MR1400612DOI10.21136/MB.1996.126102
  20. Schwabik, Š., Ye, G., 10.1142/5905, Series in Real Analysis 10. World Scientific, Hackensack (2005). (2005) Zbl1088.28008MR2167754DOI10.1142/5905
  21. Thomson, B. S., 10.1007/BFb0074380, Lecture Notes in Mathematics 1170. Springer, Berlin (1985). (1985) Zbl0581.26001MR0818744DOI10.1007/BFb0074380
  22. Ward, A. J., 10.1007/BF01180442, Math. Z. 41 (1936), 578-604. (1936) Zbl0014.39702MR1545641DOI10.1007/BF01180442

NotesEmbed ?

top

You 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.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.