Boundedness Of Weıghted Iterated Hardy-Type Operators Involvıng Suprema From Weıghted Lebesgue Spaces Into Weıghted Cesàro Functıon Spaces

In this paper the boundedness of the weighted iterated Hardy-type operators Tu,b and Tu?,b involving suprema from weighted Lebesgue space Lp(v) into weighted Cesàro function spaces Cesq(w,a) are characterized. These results allow us to obtain the characterization of the boundedness of the supremal operator Ru from Lp(v) into Cesq(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 Pu,b from Lp(v) into Cesq(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 Tu,b involving suprema from Lp(v) into Cesq(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? from ?p(v) into ?q(w). © 2020 Michigan State University Press. All rights reserved.