A Necessary and Sufficient Condition for Hardy’s Operator in the Variable Lebesgue Space
Copyright policy )A Necessary and Sufficient Condition for Hardy’s Operator in the Variable Lebesgue Space
The variable exponent Hardy inequalityxβ(x)-1∫0xf(t)dtLp(.)(0,l)≤Cxβ(x)fLp(.)(0,l),f≥0is proved assuming that the exponentsp:(0,l)→(1,∞),β:(0,l)→ℝnot rapidly oscilate near origin and1/p′(0)-β>0. The main result is a necessary and sufficient condition onp,βgeneralizing known results on this inequality.
- Yıldız Technical University Turkey
QA1-939, Inequalities involving derivatives and differential and integral operators, Mathematics, \(H^p\)-spaces, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
QA1-939, Inequalities involving derivatives and differential and integral operators, Mathematics, \(H^p\)-spaces, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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