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Hardy-type inequalities on strong and weak Orlicz-Lorentz spaces

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Abstract

In the present paper, the characterization of strong-type modular inequality

$$ \int_0^\infty {\varphi (Sf(t))w(t)dt \leqslant } \int_0^\infty {\varphi (Cf(t))w(t)dt,\forall f \downarrow } $$

is given, where φ ∈ Δ′ and S is a Hardy operator. Furthermore, the equivalent conditions of modular inequalities and norm inequalities related to weak Orlicz-Lorentz spaces are researched. We also explore the conditions for Orlicz-Lorentz spaces and weak Orlicz-Lorentz spaces to be normable. Finally, the weak boundedness of certain Hardy-type operators on Orlicz-Lorentz spaces is studied.

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  1. Department of Mathematics, Zhejiang International Studies University, Hangzhou, 310012, China

    HongLiang Li

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Li, H. Hardy-type inequalities on strong and weak Orlicz-Lorentz spaces. Sci. China Math. 55, 2493–2505 (2012). https://doi.org/10.1007/s11425-012-4456-1

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