Estimates on the (Lp(w)- Lq(w)) operator norm of the fractional maximal function

GLADIS GUADALUPE PRADOLINI; SALINAS, O. M.

REVISTA DE LA UNIóN MATEMáTICA ARGENTINA

UNION MATEMATICA ARGENTINA

Año: 1996 vol. 40 p. 69 - 74

0041-6932

In $R^n$, given, $gamma in [0, n)$ and $p in (1, n/gamma)$, it is well known that $w^q in Ar$, with $1/q = l/p - gamma/n$ and $r = 1 + q/p´$ is a necessary and sufficient condition for the boundedness of the Maximal Fractional Operator $M_{gamma}$ between $L^P(w^P)$ and $L^q(w^q)$ spaces. In this work we study the dependence of the operator norm on the constant of the Ar condition. The result extends the obtained by S. Buckley for the Hardy-Littlewood Maximal Function (i.e.: gamma= 0).