Abstract:In this paper, we give a generalization of Fefferman-Stein inequality for the fractional one-sided maximal operator: $$ \int _{-\infty }^{+\infty } M_{\alpha }^+(f)(x)^p w(x) dx \leq A_p \int _{-\infty }^{+\infty } |f(x)|^p M_{\alpha p}^-(w)(x) dx, $$ where $0 < \alpha < 1$ and $1 < p < 1/\alpha $. We also obtain a substitute of dual theorem and weighted norm inequalities for the one-sided fractional integral $I_{\alpha }^+$.
Keywords: one-sided fractional operators, weighted inequalities
AMS Subject Classification: Primary 26A33; Secondary 42B25