On absolute continuity of a modular connected with strong summability
On absolute continuity of a modular connected with strong summability
Summary: There are given sufficient conditions in order that the modular \({\mathcal A}_\Phi\), where \[ {\mathcal A}_\Phi(f)= \sup_{w\in {\mathcal W}} \int^b_a a_w(x) {\mathcal J}_\Phi(x, f) dm(x), \] with \[ {\mathcal J}_\Phi(x, f)= \int_\Omega \Phi(x, |f(t)|) d\mu(t), \] be absolutely continuous and absolutely finite.
- University of Perugia Italy
Integral operators, Modular spaces, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), absolute continuity; modular spaces; summability methods, summability method, absolute continuity, modular space, Absolute and strong summability, modular, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Integral operators, Modular spaces, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), absolute continuity; modular spaces; summability methods, summability method, absolute continuity, modular space, Absolute and strong summability, modular, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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