Revistes Catalanes amb Accés Obert (RACO)

Two weight norm inequality for the fractional maximal operator and the fractional integral operator

Y. Rakotondratsimba


New sufficient conditions on the weight functions $u(.)$ and $v(.)$ are given in order that the fractional maximal [resp. integral] operator $M_s$ [resp. $I_s$], $0\le s < n$, [resp. $0 < s < n$] sends the weighted Lebesgue space $L^p(v(x)\,dx)$ into $L^p(u(x)\,dx)$, $1 < p < \infty$. As a consequence a characterization for this estimate is obtained whenever the weight functions are radial monotone.

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