Some aspects of $L_{w_1 }^r $(G) ∩ L(p,q,w ₂dµ)(G)

Abstract

Let G be a locally compact Abelian group with Haar measure. The authors discuss some basic properties of $L_{w_1 }^r $(G) ∩ L(p,q,w ₂dµ)(G) spaces. Then the necessary conditions for compact embeddings of the spaces $L_{w_1 }^r $(R ^d)∩L(p,q,w ₂dµ)(R ^d) are showed.

Keywords

Weighted Lebesgue spaces / Weighted Lorentz spaces / Compact embeddings

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