On the boundedness of the maximal and fractional maximal, potential operators in the Global Morrey-type spaces with variable exponents

We consider the global Morrey-type spaces ${GM}_{p(\cdot),\theta(\cdot),w(\cdot)}(\Omega)$ with variable exponents $p(x)$, $\theta(x)$ and general function $w(x,r)$ defining these spaces. In the case of unbounded sets $\Omega\subset{\mathbb{R}}^{n}$, we prove boundedness of the Hardy–Littlewood maximal operator and potential type operator in these spaces. We prove Spanne-type results on the boundedness of the Riesz potential ${I}^{\alpha}$ in global Morrey-type spaces with variable exponent ${GM}_{p(\cdot),\theta(\cdot),w(\cdot)}(\Omega)$.