Weighted norm inequalities for fractional maximal operators - a Bellman function approach Rodrigo BanuelosAdam Osekowski 42B20Weighted norm inequalities We study classical weighted $L^p\to L^q$ inequalities for the fractional maximal operators on $\mathbb{R}^d$, proved originally by Muckenhoupt and Wheeden in the 1970s. We establish a slightly stronger version of this inequality with the use of a novel extension of Bellman function method. More precisely, the estimate is deduced from the existence of a certain special function that enjoys appropriate majorization and concavity. From this result and an explicit version of the $A_{p-\varepsilon}$ theorem," derived also with Bellman functions, we obtain the sharp inequality of Lacey, Moen, P\'erez, and Torres. Indiana University Mathematics Journal 2015 text pdf 10.1512/iumj.2015.64.5534 10.1512/iumj.2015.64.5534 en Indiana Univ. Math. J. 64 (2015) 957 - 972 state-of-the-art mathematics http://iumj.org/access/