Boundedness of weighted iterated Hardy-type operators involving suprema from weighted Lebesgue spaces into weighted Cesàro function spaces

2019/02/27 by Rza Mustafayev, Nevin Bilgiçli
Mathematics · #math.FA #msc:46E30 #msc:26D10 #msc:42B25 #msc:42B35

paper · pdf · doi:10.14321/realanalexch.45.2.0339

published as Real Anal. Exchange, Volume 45, Number 2 (2020), 339-374 · 26 pages. arXiv admin note: text overlap with arXiv:1109.5400 by other authors

arxiv created 2019/02/27 · arxiv updated 2020/08/12

Abstract

In this paper 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 Cesàro function spaces 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 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 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 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_γ from Λ^p(v) into Γ^q(w).

Citations

• On the dual of Cesàro function space