Note on functions satisfying the integral Holder condition

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 $\Bbb R$ 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 $1$.

Keywords: integral modulus of continuity, variation of a function

Classification (MSC91): 26A15, 26A45, 26A16

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