Geodesic
Note on functions satisfying the integral Hölder condition
Mathematica Bohemica, Tome 121 (1996) no. 3, pp. 263-268

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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 $1$.
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 $1$.
DOI : 10.21136/MB.1996.125989
Classification : 26A15, 26A16, 26A45
Keywords: integral modulus of continuity; variation of a function 
Král, Josef, Jr. Note on functions satisfying the integral Hölder condition. Mathematica Bohemica, Tome 121 (1996) no. 3, pp. 263-268. doi: 10.21136/MB.1996.125989
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