Weak estimates for the maximal and Riesz potential operators in central Herz-Morrey spaces on the unit ball (Q2039395)

This nice paper introduces the weak central Herz-Morrey spaces \(WH^{p(\cdot),q,\omega}(\mathbf B)\) and \(WH^{p^\ast(\cdot),q,\omega}(\mathbf B)\) with \( p^\ast(x) = p(x)N/(N-\alpha p(x))\) on the Euclidean unit ball \(\mathbf B\) and shows the boundedness of the generalized maximal operator \(M_\beta\) and the Riesz potential operator \(I_\alpha\) from the non-homogeneous central Herz-Morrey space \(H^{p(\cdot),q,\omega}(\mathbf B)\) to \(WH^{p(\cdot),q,\omega}(\mathbf B)\) (Theorem 3.10) and \(WH^{p^\ast(\cdot),q,\omega}(\mathbf B)\) (Theorem 4.1), respectively.