Weighted inequalities involving Hardy and Copson operators
نویسندگان
چکیده
We characterize a four-weight inequality involving the Hardy operator and Copson operator. More precisely, given p1,p2,q1,q2?(0,?), we find necessary sufficient conditions on non-negative measurable functions u1,u2,v1,v2 (0,?) for which there exists positive constant c such that inequality(?0?(?0tf(s)p2v2(s)p2ds)q2p2u2(t)q2dt)1q2?c(?0?(?t?f(s)p1v1(s)p1ds)q1p1u1(t)q1dt)1q1 holds every function f (0,?). The proof is based discretizing antidiscretizing techniques. principal innovation consists in development of new method carefully avoids duality techniques therefore enables us to obtain characterization previously unavailable situations, solving thereby long-standing open problem. then apply establishing criteria embeddings between weighted spaces Copp1,q1(u1,v1) Cesàro Cesp2,q2(u2,v2), also Sq(w) equipped with norm ?f?Sq(w)=(?0?[f??(t)?f?(t)]qw(t)dt)1/q classical Lorentz type ?.
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2022
ISSN: ['0022-1236', '1096-0783']
DOI: https://doi.org/10.1016/j.jfa.2022.109719