The preduals of Banach space valued Bourgain-Morrey spaces

2025/05/25 by Bai, Tengfei, Guo, Pengfei, Xu, Jingshi
#42B25 #42B35 #46E30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2505.19143

Abstract

Let X be a Banach space such that there exists a Banach space ^∗ X and ( ^∗ X )^ ∗ = X . In this paper, we introduce X-valued Bourgain-Morrey spaces. We show that ^∗ X-valued block spaces are the predual of X-valued Bourgain-Morrey spaces. We obtain the completeness, denseness and Fatou property of ^∗ X-valued block spaces. We give a description of the dual of X-valued Bourgain-Morrey spaces and conclude the reflexivity of these spaces. The boundedness of powered Hardy-Littlewood maximal operator in vector valued block spaces is obtained.

Citations

• Precompactness in matrix weighted Bourgain-Morrey spaces
• Two minimization problems on non-scattering solutions to mass-subcritical nonlinear Schrödinger equation
• Tent Space Boundedness Via Extrapolation
• Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg-de Vries equation
• On the boundedness of singular integrals in Morrey spaces and its preduals
• The Fatou property of block spaces

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