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Riemann-Liouville and higher dimensional Hardy operators for nonnegative decreasing function in \(L^{p(\cdot)}\) spaces. (English) Zbl 1474.42089

Summary: One-weight inequalities with general weights for Riemann-Liouville transform and \(n\)-dimensional fractional integral operator in variable exponent Lebesgue spaces defined on \(\mathbb{R}^n\) are investigated. In particular, we derive necessary and sufficient conditions governing one-weight inequalities for these operators on the cone of nonnegative decreasing functions in \(L^{p(x)}\) spaces.

MSC:

42B30 \(H^p\)-spaces
26A33 Fractional derivatives and integrals
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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