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Article · Siberian Advances in Mathematics · May 1, 2022

On the Boundedness of Integral Operators in Morrey-Type Spaces with Variable Exponents

Nurzhan Bokayev, Zh. M. Onerbek

Nurzhan Bokayev
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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 $$ {GM}_{p(\cdot ),\theta (\cdot ),w(\cdot )}(\Omega ) $$ .

Advanced Harmonic Analysis ResearchNonlinear Partial Differential EquationsMathematical Analysis and Transform Methodsvariable exponentintegral operatorsHardy-Littlewood maximal operator

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