| Title:
|
Note on functions satisfying the integral Hölder condition (English) |
| Author:
|
Král, Josef, Jr. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
121 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
263-268 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Given a modulus of continuity $\omega$ and $q \in[1, \infty[ $ then $H_q^\omega$ denotes the space of all functions $f$ with the period $1$ on $\R$ that are locally integrable in power $q$ and whose integral modulus of continuity of power $q$ (see(1)) is majorized by a multiple of $ \omega$. The moduli of continuity $ \omega$ are characterized for which $H_q^\omega$ contains "many" functions with infinite "essential" variation on an interval of length $1$. (English) |
| Keyword:
|
integral modulus of continuity |
| Keyword:
|
variation of a function |
| MSC:
|
26A15 |
| MSC:
|
26A16 |
| MSC:
|
26A45 |
| idZBL:
|
Zbl 0863.26006 |
| idMR:
|
MR1419879 |
| DOI:
|
10.21136/MB.1996.125989 |
| . |
| Date available:
|
2009-09-24T21:19:18Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125989 |
| . |
| Reference:
|
[1] O. Kováčik: A necessary condition of embedding of $H_p^{\omega}$ into the space of functions with bounded variations.Izvestija vysšich učebnych zaveděnij Matematika 10 (1983), 26-28. (In Russian.) |
| Reference:
|
[2] W. Orlicz: Application of Baire's category method to certain problems of mathematical analysis.Wiadomości Matematyczne XXIV (1982), 1-15. (In Polish.) MR 0705608 |
| Reference:
|
[3] J. C. Oxtoby: Mass und Kategorie.Springeг-Verlag, 1971. Zbl 0217.09202, MR 0393404 |
| Reference:
|
[4] A. F. Timan: Theory of Approximation of function of Real Variable.Moskva, 1960. (In Russian.) |
| Reference:
|
[5] G. H. Hardy J. E. Littlewood: Some properties of fractional integrals I, II.Math. Z. 27 (1928), 565-606; З4 (1932), 403-439. MR 1544927 |
| . |
