Bounds for the maximal and Riesz potential operators with variable fractionality

Francisco Gonçalves, Tuomas Oikari

We prove $L^{p(\cdot )}$-to-$L^{q(\cdot )}$ bounds for variable versions of the fractional maximal $M^{\alpha (\cdot )}$ and Riesz potential $I^{\alpha (\cdot )}$ operators. The changing fractiona…