AI 中文总结
本文证明了Besov-Morrey和Triebel-Lizorkin-Morrey空间的Hölder不等式，推广了Sickel与Triebel1995年的结果，采用仿乘运算及Franke-Jawerth嵌入完成证明。
AI 中文摘要
本文证明了Besov-Morrey空间$ \mathcal{N}^{s}_{u,p,q}(\mathbb{R}^{d}) $和Triebel-Lizorkin-Morrey空间$ \mathcal{E}^{s}_{u,p,q}(\mathbb{R}^{d}) $的Hölder不等式。研究发现，当满足包含$s > d \max ( 0, \frac{1}{p} - 1) $的参数相关特定条件时，这些Morrey光滑空间是逐点乘子空间。在此背景下，该研究显著推广了Sickel和Triebel于1995年得到的原始Besov与Triebel-Lizorkin空间的Hölder不等式。证明过程中使用了仿乘运算以及Haroske和Skrzypczak得到的一些Franke-Jawerth嵌入。
英文摘要
In this paper we prove Hölder inequalities for the Besov-Morrey spaces $ \mathcal{N}^{s}_{u,p,q}(\mathbb{R}^{d}) $ and the Triebel-Lizorkin-Morrey spaces $ \mathcal{E}^{s}_{u,p,q}(\mathbb{R}^{d}) $. We observe that these Morrey smoothness spaces are pointwise multiplier spaces if certain conditions concerning the parameters also including $ s > d \max ( 0, \frac{1}{p} - 1) $ are fulfilled. In this context we significantly generalize the Hölder inequalities for the original Besov and Triebel-Lizorkin spaces obtained by Sickel and Triebel in 1995. For the proofs we use paramultiplication and some Franke-Jawerth embeddings obtained by Haroske and Skrzypczak.
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