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Extension in generalized Orlicz spaces. (English) Zbl 1457.46038

Summary: We prove that a \(\Phi\)-function can be extended from a domain \(\Omega\) to all of \(\mathbb{R}^n\) while preserving crucial properties for harmonic analysis on the generalized Orlicz space \(L^\Phi\).

MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
26B25 Convexity of real functions of several variables, generalizations
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