On the boundedness of the maximal operator and the Riesz potential in global Morrey-type spaces with variable exponents on unbounded domains

We consider global Morrey-type spaces with variable exponents $GM_{p(.),\theta(.),w(.)}(\Omega)$ on unbounded domains $\Omega$. Conditions are given for the variable parameters defining the indicated spaces, under which the maximal operator and the Riesz potential with variable exponents are bounded in these spaces.