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Let L0(T) be the set of real-valued periodic measurable functions, let Ψ: R+→ R+ be the modulus of continuity, and letLΨ≡LΨT=f∈L0T:fΨ≔12π∫TΨfxdx Click to show full abstract
Let L0(T) be the set of real-valued periodic measurable functions, let Ψ: R+→ R+ be the modulus of continuity, and letLΨ≡LΨT=f∈L0T:fΨ≔12π∫TΨfxdx<∞.$$ {L}_{\Psi}\equiv {L}_{\Psi}(T)=\left\{f\in {L}_0(T):{\left\Vert f\right\Vert}_{\Psi}\coloneq \frac{1}{2\uppi}\underset{T}{\int}\Psi \left(\left|f(x)\right|\right) dx<\infty \right\}. $$ We study the properties of multiple moduli of continuity for the functions from LΨ.
Keywords:
psi;
periodic functions;
moduli continuity;
continuity;
continuity periodic;
properties moduli
Journal Title: Ukrainian Mathematical Journal
Year Published: 2017
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Journal Title: Ukrainian Mathematical Journal
Year Published: 2017
Link to full text (if available)
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recommendations!