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arXiv · 2606.22139

On Block Spaces on the Unit Sphere

Laith Hawawsheh·Ahmad Al-Salman·Yibiao Pan
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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 $L(\log L)^{1+v}$ by demonstrating that $B_q^{0,v}$ is a proper subspace of $L(\log L)^{1+v}$. Furthermore, we prove that the union of all block spaces $B_q^{0,v}$ for $1 < q \le \infty$ is strictly contained within $L(\log L)^{1+v}$.

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Laith Hawawsheh, Ahmad Al-Salman, Yibiao Pan. 2026-06-20. On Block Spaces on the Unit Sphere. https://arxiv.org/abs/2606.22139

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