Morrey Spaces are Embedded Between Weak Morrey Spaces and Stummel Classes

Nicky Tumalun, Hendra Gunawan

Abstract


In this paper, we show that the Morrey spaces $ L^{1,\left( \frac{\lambda}{p} -
\frac{n}{p} + n \right) } \left( \mathbb{R}^{n} \right) $ are embedded between
weak Morrey spaces $ wL^{p,\lambda}\left( \mathbb{R}^{n} \right) $ and Stummel
classes $ S_{\alpha}\left( \mathbb{R}^{n} \right) $ under some conditions on
$ p, \lambda $ and $ \alpha $. More precisely, we prove that $ wL^{p,\lambda}\left(
\mathbb{R}^{n} \right) \subseteq L^{1,\left( \frac{\lambda}{p} - \frac{n}{p} + n
\right) } \left( \mathbb{R}^{n} \right) \subseteq S_{\alpha}\left( \mathbb{R}^{n}
\right) $ where $ 1<p<\infty, 0<\lambda<n $ and $ \frac{n-\lambda}{p}<\alpha<n $.
We also show that these inclusion relations under the above conditions are proper.
Lastly, we present an inequality of Adams' type \cite{A}


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DOI: https://doi.org/10.22342/jims.1.1.817.33-40

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Journal of the Indonesian Mathematical Society
Mathematics Department, Universitas Gadjah Mada
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p-ISSN: 2086-8952 | e-ISSN: 2460-0245


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