# Article

 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 .

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