Boundedness of the fractional Hardy-Littlewood maximal operator on weighted Morrey spaces

Abstract

We prove the strong type boundedness of the fractional Hardy-Littlewood maximal operator from weighted Morrey spaces $L^{p,(\lambda _{1},\lambda _{2})}(|x|^{\beta p}\omega ^{p})$ to $L^{q,(q(\lambda _{1}+\lambda _{2})/p-\lambda _{2},\lambda _{2})} (|x|^{\beta q}\omega ^{q})$ for $p>1$ and $\omega \in A(p,q)$. We also obtain the weak type estimate for $p=1$ and $\omega \in A(1,q)$.