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- W2912133962 abstract "Abstract Let ρ be a monotone quasinorm defined on ${rm {frak M}}^ + $ , the set of all non-negative measurable functions on [0, ∞). Let T be a monotone quasilinear operator on ${rm {frak M}}^ + $ . We show that the following inequality restricted on the cone of λ -quasiconcave functions $$rho (Tf) les C_1left( {int_0^infty {f^p} v} right)^{1/p},$$ where $1les ples infty $ and v is a weighted function, is equivalent to slightly different inequalities considered for all non-negative measurable functions. The case 0 < p < 1 is also studied for quasinorms and operators with additional properties. These results in turn enable us to establish necessary and sufficient conditions on the weights ( u , v , w ) for which the three weighted Hardy-type inequality $$left( {int_0^infty {{left( {int_0^x f u} right)}^q} w(x){rm d}x} right)^{1/q} les C_1left( {int_0^infty {f^p} v} right)^{1/p},$$ holds for all λ -quasiconcave functions and all 0 < p , q ⩽ ∞." @default.
- W2912133962 created "2019-02-21" @default.
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- W2912133962 date "2019-01-23" @default.
- W2912133962 modified "2023-10-18" @default.
- W2912133962 title "Weighted norm inequalities for positive operators restricted on the cone of λ-quasiconcave functions" @default.
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- W2912133962 doi "https://doi.org/10.1017/prm.2018.85" @default.
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