Embeddability of ℓ_p-spaces into mixed-norm Lebesgue spaces in connection with the validity of vector-valued extensions of the Riesz--Fischer Theorem

2025/02/19 by Ansorena, José L., Bello, Glenier
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2502.13561

Abstract

The aim of this paper is twofold. On the one hand, we compute, in terms of r and s, the indices p for which ℓ_p isomorphically embeds into the mixed-norm separable spaces L_s(L_r), ℓ_s(L_r), L_s(ℓ_r) and ℓ_s(ℓ_r). On the other hand, we use this information to move forward in the isomorphic classification of mixed-norm spaces. In particular, we tell apart the spaces L₂(L_r) and ℓ₂(L_r), r\not=2.

Related

• Mutually non isomorphic mixed-norm Lebesgue spaces
• Mixed-Norm Herz Spaces and Their Applications in Related Hardy Spaces
• On Function Spaces with Mixed Norms --- A Survey
• Optimal rearrangement invariant Sobolev embeddings in mixed norm spaces
• Mixed-norm Herz-type Besov-Triebel-Lizorkin spaces