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Local sharp maximal functions, geometrical maximal functions and rough maximal functions on local Morrey spaces with variable exponents. (English) Zbl 1457.42034

In the paper under review the authors obtain that the dual space of the local block space with variable exponent is the local Morrey space with variable exponent. They also obtain the boundedness of the Hardy-Littlewood maximal operators on the local block spaces with variable exponents. With these results, they extend the extrapolation theory to the local Morrey spaces with variable exponents. As applications, they obtain the mapping properties of the rough maximal function, the local sharp maximal function and the geometric maximal operator on local Morrey spaces with variable exponents.

MSC:

42B25 Maximal functions, Littlewood-Paley theory
42B35 Function spaces arising in harmonic analysis
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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