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Interpolation theorems for variable exponent Lebesgue spaces. (English) Zbl 1202.46024

The classical result of Fefferman and Stein about complex interpolation between the Lebesgue space \(L^p\) on \({\mathbb R}^n\) and the spaces \(BMO\) or \(H^1\) is extended to the case of variable exponents \(p(.)\), under the condition that the Hardy-Littlewood maximal operator is bounded in \(L^{p(.)}\).

MSC:

46B70 Interpolation between normed linear spaces
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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