Some embeddings of Morrey spaces with critical smoothness

2019/05/23 by Haroske, Dorothee D., Moura, Susana D., Skrzypczak, Leszek · 2 citations
#46E35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1905.09703

Abstract

We study embeddings of Besov-Morrey spaces \cal N^s_u,p,q(\mathbb R^d) and of Triebel-Lizorkin-Morrey spaces \cal E^s_u,p,q(\mathbb R^d) in the limiting cases when the smoothness s equals s₀=dmax(1/u-p/u,0) or s_∞=d/u, which is related to the embeddings in L₁^loc(\mathbb R^d) or in L_∞(\mathbb R^d), respectively. When s=s₀ we characterise the embeddings in L₁^loc(\mathbb R^d) and when s=s_∞ we obtain embeddings into Orlicz-Morrey spaces of exponential type and into generalised Morrey spaces.

Cited by

• On the boundedness of dilation operators in the context of Triebel-Lizorkin-Morrey spaces
• Sharp Brezis--Seeger--Van Schaftingen--Yung Formulae for Higher-Order Gradients in Ball Banach Function Spaces

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