Morrey Spaces are Embedded Between Weak Morrey Spaces and Stummel Classes - Tumalun, Nicky; Gunawan, Hendra (Journal of the Indonesian Mathematical Society, 2019)
In this paper, we show that the Morrey spaces $ L^{1,\left( \frac{λ}{p} -\frac{n}{p} + n \right) } \left( \mathbb{R}^{n} \right) $ are embedded betweenweak Morrey spaces $ wL^{p,λ}\left( \mathbb{R}^{n} \right) $ and Stummelclasses $ S_{α}\left( \mathbb{R}^{n} \right) $ under some conditions on$ p, λ $ and $ α $. More precisely, we prove that $ wL^{p,λ}\left(\mathbb{R}^{n} \right) \subseteq L^{1,\left( \frac{λ}{p} - \frac{n}{p} + n\right) } \left( \mathbb{R}^{n} \right) \subseteq S_{α}\left( \mathbb{R}^{n}\right) $ where $ 1p∞, 0\lambdan $ and $ \frac{n-λ}{p}\alphan $.We also show that these inclusion relations under the above conditions are proper.Lastly, we present an inequality of Adams' type \cite{A}