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Investigates the continuity of generalized maximal functions, exploring implications for integration sets.
We generalize the centered and uncentered Hardy-Littlewood maximal function in terms of shape of integration sets. Continuity of two global and two local generalized maximal functions in Rⁿ R n is studied. The global ones are continuous. One of the local ones is continuous, provided the integration set is star-shaped with respect to its center. For the second local one, we construct a counterexample.
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Juha Kapulainen (2026) studied this question.
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