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- W2791777215 abstract "Morrey norms, which are originally endowed with two parameters, are considered on general metric measure spaces. Volberg, Nazarov and Treil showed that the modified Hardy-Littlewood maximal operator is bounded on Legesgue spaces. The modified Hardy-Littlewood maximal operator is known to be bounded on Morrey spaces on Euclidean spaces, if we introduce the third parameter instead of adopting a natural extension of Morrey spaces. When it comes to geometrically doubling, as long as an auxiliary parameter is introduced suitably, the Morrey norm does not depend on the third parameter and this norm extends naturally the original Morrey norm. If the underlying space has a rich geometric structure, there is still no need to introduce auxiliary parameters. However, an example shows that this is not the case in general metric measure spaces. In this paper, we present an example showing that Morrey spaces depend on the auxiliary parameters." @default.
- W2791777215 created "2018-03-29" @default.
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- W2791777215 date "2018-02-01" @default.
- W2791777215 modified "2023-10-16" @default.
- W2791777215 title "A remark on modified Morrey spaces on metric measure spaces" @default.
- W2791777215 doi "https://doi.org/10.14492/hokmj/1520928055" @default.
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