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Keywords:
one-sided fractional operators; weighted inequalities
one-sided fractional operators; weighted inequalities
Summary:
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 $I_{\alpha}^+$.
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