an:07229051
Zbl 07229051
Mustafayev, Rza; Bilgi??li, Nevin
Boundedness of weighted iterated Hardy-type operators involving suprema from weighted Lebesgue spaces into weighted Ces??ro function spaces
EN
Real Anal. Exch. 45, No. 2, 339-374 (2020).
00451575
2020
j
46E30 26D10 42B25 42B35
weighted iterated Hardy operators involving suprema; Ces??ro function spaces; fractional maximal functions; classical Lorentz spaces
Summary: The boundedness of the weighted iterated Hardy-type operators \(T_{u,b}\) and \(T_{u,b}^*\) involving suprema from weighted Lebesgue space \(L_p(v)\) into weighted Ces??ro function spaces \({\operatorname{Ces}}_q(w,a)\) are characterized. These results allow us to obtain the characterization of the boundedness of the supremal operator \(R_u\) from \(L^p(v)\) into \({\operatorname{Ces}}_q(w,a)\) on the cone of monotone non-increasing functions. For the convenience of the reader, we formulate the statement on the boundedness of the weighted Hardy operator \(P_{u,b }\) from \(L^p(v)\) into \({\operatorname{Ces}}_q(w,a)\) on the cone of monotone non-increasing functions. Under additional condition on \(u\) and \(b\), we are able to characterize the boundedness of weighted iterated Hardy-type operator \(T_{u,b}\) involving suprema from \(L^p(v)\) into \({\operatorname{Ces}}_q(w,a)\) on the cone of monotone non-increasing functions. At the end of the paper, as an application of obtained results, we calculate the norm of the fractional maximal function \(M_{\gamma}\) from \(\Lambda^p(v)\) into \(\Gamma^q(w)\).