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 \( {GM}_{p(\cdot ),\theta (\cdot ),w(\cdot )}(\Omega ) \).
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Bokayev, N.A., Onerbek, Z.M. On the Boundedness of Integral Operators in Morrey-Type Spaces with Variable Exponents. Sib. Adv. Math. 32, 79–86 (2022). https://doi.org/10.1134/S1055134422020018
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DOI: https://doi.org/10.1134/S1055134422020018