Let $\mu$ be a non-negative Borel measure on $\mathbb{R}^d$ which only satisfies some growth condition, we study two-weight norm inequalities for fractional maximal functions associated to such $\mu$. A necessary and sufficient condition for the maximal operator to be bounded from $L^p(v)$ into weak $L^{q}(u)$ $(1 \leq p \leq q \lt \infty)$ is given. Furthermore, by using certain Orlicz norm, a strong type inequality is obtained.
Taiwanese J. Math.
16(4):
1409-1422
(2012).
DOI: 10.11650/twjm/1500406741