Note on functions satisfying the integral Hölder condition

Josef, Jr. Král

Mathematica Bohemica (1996)

  • Volume: 121, Issue: 3, page 263-268
  • ISSN: 0862-7959

Abstract

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Given a modulus of continuity ω and q ∈ [ 1 , ∞ [ then H q ω 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 ω . The moduli of continuity ω are characterized for which H q ω contains “many” functions with infinite “essential” variation on an interval of length 1 .

How to cite

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Král, Josef, Jr.. "Note on functions satisfying the integral Hölder condition." Mathematica Bohemica 121.3 (1996): 263-268. <http://eudml.org/doc/247974>.

@article{Král1996,
abstract = {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 $\mathbb \{R\}$ 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 $1$.},
author = {Král, Josef, Jr.},
journal = {Mathematica Bohemica},
keywords = {integral modulus of continuity; variation of a function; integral modulus of continuity; variation of a function},
language = {eng},
number = {3},
pages = {263-268},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Note on functions satisfying the integral Hölder condition},
url = {http://eudml.org/doc/247974},
volume = {121},
year = {1996},
}

TY - JOUR
AU - Král, Josef, Jr.
TI - Note on functions satisfying the integral Hölder condition
JO - Mathematica Bohemica
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 121
IS - 3
SP - 263
EP - 268
AB - 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 $\mathbb {R}$ 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 $1$.
LA - eng
KW - integral modulus of continuity; variation of a function; integral modulus of continuity; variation of a function
UR - http://eudml.org/doc/247974
ER -

References

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  1. O. Kováčik, A necessary condition of embedding of H p ω into the space of functions with bounded variations, Izvestija vysšich učebnych zaveděnij Matematika 10 (1983), 26-28. (In Russian.) (1983) 
  2. W. Orlicz, Application of Baire's category method to certain problems of mathematical analysis, Wiadomości Matematyczne XXIV (1982), 1-15. (In Polish.) (1982) MR0705608
  3. J. C. Oxtoby, Mass und Kategorie, Springeг-Verlag, 1971. (1971) Zbl0217.09202MR0393404
  4. A. F. Timan, Theory of Approximation of function of Real Variable, Moskva, 1960. (In Russian.) (1960) 
  5. G. H. Hardy J. E. Littlewood, Some properties of fractional integrals I, II, Math. Z. 27 (1928), 565-606; З4 (1932), 403-439. (1928) MR1544927

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