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arXiv · 2506.07478

On Herz-Bochkarev limiting problem

Erlan Nursultanov·Arash Ghorbanalizadeh·Durvudkhan Suragan
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Abstract

This paper studies Hausdorff-Young-type inequalities within the framework of Lorentz spaces $L_{p,q}$. Focusing on the dependence of the associated constants on the integrability parameter $p$, we derive optimal bounds in the limiting case $p\rightarrow 2$, addressing the Herz-Bochkarev problem. The results obtained refine the pioneering estimates in [3] and are comparable to recent advances in [16]. The main ingredients of our approach are new grand Lorentz space techniques.

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Erlan Nursultanov, Arash Ghorbanalizadeh, Durvudkhan Suragan. 2025-06-09. On Herz-Bochkarev limiting problem. https://arxiv.org/abs/2506.07478

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