Geodesic
Two weight norm inequalities for fractional one-sided maximal and integral operators
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 1, pp. 35-46

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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 $I_{\alpha}^+$.
Classification : 26A33, 26D10, 42B25
Keywords: one-sided fractional operators; weighted inequalities 
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De Rosa, Liliana. Two weight norm inequalities for fractional one-sided maximal and integral operators. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 1, pp. 35-46. http://geodesic.mathdoc.fr/item/CMUC_2006__47_1_a3/