A weighted variant of Riemann-Liouville fractional integrals on \(\mathbb R^n\) (Q1925429)

Summary: We introduce certain type of weighted variant of Riemann-Liouville fractional integral on \(\mathbb R^n\) and obtain its sharp bounds on the central Morrey and \(\lambda\)-central BMO spaces. Moreover, we establish a sufficient and necessary condition of the weight functions so that commutators of weighted Hardy operators (with symbols in \(\lambda\)-central BMO space) are bounded on the central Morrey spaces. These results are further used to prove sharp estimates of some inequalities due to Weyl and Cesàro.