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Grand Morrey Spaces and Grand Hardy–Morrey Spaces on Euclidean Space
The Journal of Geometric Analysis, 2023In this paper, the author introduces and investigates grand Morrey spaces and grand Hardy-Morrey spaces on \(\mathbb R^n\). He shows that whenever a grand Morrey space satisfies some mild conditions, the characteristic functions of balls belong to a grand Morrey space. Hence, a grand Morrey space is a ball Banach function space.
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The author gives a necessary and sufficient condition of pointwise multipliers between Morrey spaces. The Morrey space \(\dot{M}^{p,q}=\dot{M}^{p,q}(\mathbb{R}^d)\) is defined by \[ \sup_{Q \in \mathcal{Q}}R_{Q}^{d/q-d/p}\biggl(\int_{Q}|f(x)|^p \;dx \biggr)^{1/p}< \infty \] with the norm \(||f||_{\dot{M}^{p,q}}=\sup_{Q \in \mathcal{Q}}R_{Q}^{d/q-d/p ...
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Besov‐Morrey spaces and Triebel‐Lizorkin‐Morrey spaces on domains
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Zeitschrift für Analysis und ihre Anwendungen, 2017The generalized Morrey space {\mathcal M}_{p,\phi}({\mathbb R}^n) was defined by Mizuhara 1991 and Nakai in 1994. It is equipped with a parameter 0 < p < \infty
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