Maximal and Potential Operators in Variable Exponent Morrey Spaces

Abstract We prove the boundedness of the Hardy–Littlewood maximal operator on variable Morrey spaces 𝐿𝑝(·), λ(·)(Ω) over a bounded open set Ω ⊂ ℝ𝑛 and a Sobolev type 𝐿𝑝(·), λ(·) → 𝐿𝑞(·), λ(·)-theorem for potential operators 𝐼 α(·), also of variable order. In the case of constant α, the limiting case is also studied when the potential operator 𝐼 α acts into BMO space.

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