2021/07/22 by A. H. Kalidolday, Kalidolday, A. H., Ерлан Нурсултанов +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration
paper · pdf · doi:10.48550/arxiv.2107.10633
openalex publication_date 2021/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper studies the interpolation properties of net spaces Np,q(M), when M is the set of dyadic cubes in ℝn, and also when M is the family of all cubes with parallel faces to the coordinate axes in ℝn. It is shown that, in the case when M is the set of dyadic cubes the scale of spaces is closed with respect to the real interpolation method. In the case, when M is the set of all cubes with parallel faces to the coordinate axes, an analogue of the Marcinkiewicz-Calderon theorem on cones of non-negative functions is given.