On Block Spaces on the Unit Sphere

Laith Hawawsheh; Ahmad Al-Salman; Yibiao Pan

paper

On Block Spaces on the Unit Sphere

arXiv:2606.22139

Abstract

In this paper, we establish several properties of the block spaces $B_{q}^{0, v}$ . Our primary contribution resolves an open question regarding the relationship between $B_{q}^{0, v}$ and the Zygmund-type space $L (lo g L)^{1 + v}$ by demonstrating that $B_{q}^{0, v}$ is a proper subspace of $L (lo g L)^{1 + v}$ . Furthermore, we prove that the union of all block spaces $B_{q}^{0, v}$ for $1 < q \leq \infty$ is strictly contained within $L (lo g L)^{1 + v}$ .