Journal of the Indonesian Mathematical Society
Volume 25 Number 3 (November 2019)

Morrey Spaces are Embedded Between Weak Morrey Spaces and Stummel Classes

Tumalun, Nicky (Unknown)
Gunawan, Hendra (Unknown)



Article Info

Publish Date
31 Oct 2019

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 betweenweak Morrey spaces $ wL^{p,\lambda}\left( \mathbb{R}^{n} \right) $ and Stummelclasses $ 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 $ 1p\infty, 0\lambdan $ and $ \frac{n-\lambda}{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}

Copyrights © 2019






Journal Info

Abbrev

JIMS

Publisher

Subject

Mathematics

Description

Journal of the Indonesian Mathematical Society disseminates new research results in all areas of mathematics and their applications. Besides research articles, the journal also receives survey papers that stimulate research in mathematics and their ...