Abstract
We consider the global Morrey-type spaces $${GM}_{p(\cdot ),\theta (\cdot ),w(\cdot )}(\Omega )$$ with variable exponents $$p(x) $$ , $$\theta (x)$$ , and $$w(x,r) $$ defining these spaces. In the case of unbounded sets $$\Omega \subset {\mathbb {R}}^{n}$$ , we prove the 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 exponents $$ {GM}_{p(\cdot ),\theta (\cdot ),w(\cdot )}(\Omega ) $$ .