On Herz-Bochkarev limiting problem

2025/06/09 by Ерлан Нурсултанов, Nursultanov, Erlan, Arash Ghorbanalizadeh +3 · 1 citation
Mathematics · #42A16 #42B35 #46E30 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2506.07478

openalex publication_date 2025/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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→ 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.

Citations

• Convolution-type operators in grand Lorentz spaces
• The Fourier transform is an extremizer of a class of bounded operators
• Improved Stein inequalities for the Fourier transform
• Extensions of the vector-valued Hausdorff-Young inequalities
• Interpolation of linear operators

Cited by

• Bochkarev's inequalities in the Anisotropic grand Lorentz Spaces

Related

• Bochkarev's inequalities in the Anisotropic grand Lorentz Spaces
• Bohnenblust-Hille inequalities for Lorentz spaces via interpolation
• Real Interpolation method, Lorentz spaces and refined Sobolev inequalities
• Convolution-type operators in grand Lorentz spaces
• An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces