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

Autores: Yves Rakotondratsimba
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 42, Nº 1, 1998, págs. 81-101
Idioma: inglés
DOI: 10.5565/publmat_42198_03
Títulos paralelos:
- Dos desigualdades de norma de peso para el operador fraccional máximo y el operador fraccional integral
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Resumen
- 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.