Resumen de Weighted inequalities for integral operators on Lebesgue and BMO^{\gamma }(\omega ) spaces

Elida V. Ferreyra, Guillermo J. Flores

• We characterize the power weights \omega for which the fractional type operator T_{\alpha ,\beta } is bounded from L^p (\omega ^p) into L^q (\omega ^q) for 1< p < n/(n- (\alpha + \beta )) and 1/q = 1/p - (n- (\alpha + \beta ))/n. If n/(n-(\alpha + \beta )) \le p < n/(n -(\alpha +\beta ) -1)^{+} we prove that T_{\alpha ,\beta } is bounded from a weighted weak L^p space into a suitable weighted BMO^\delta space for weights satisfying a doubling condition and a reverse Hölder condition. Also, we prove the boundedness of T_{\alpha ,\beta } from a weighted local space BMO_{0}^{\gamma } into a weighted BMO^\delta space, for weights satisfying a doubling condition.