RUS  ENG
Full version
JOURNALS // Eurasian Mathematical Journal // Archive
Eurasian Math. J., 2023 Volume 14, Number 4, Pages 47–62 (Mi emj483)
Two–dimensional bilinear inequality for rectangular Hardy operator and non–factorizable weights

R. Senguptaab, E. P. Ushakovac

a Laboratory of approximate methods and functional analysis, Computing Center of Far Eastern branch of Russian Academy of Sciences, 65 Kim Yu Chena St., Khabarovsk 680000, Russian Federation
b Laboratory of quantum algorithms for machine learning and optimisation, Center for Artificial Intelligence Technology, Skolkovo Institute of Science and Technology, the territory of the Innovation Center "Skolkovo", Bolshoy Boulevard, 30, p.1, Moscow 121205, Russian Federation
c Laboratory of optimal controlled systems, V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya St., Moscow 117997, Russian Federation

Abstract: Necessary conditions and sufficient conditions are given for the validity of two–dimensional bilinear norm inequalities with rectangular Hardy operators in weighted Lebesgue spaces. The results are applicable for non–factorizable weights.

Keywords and phrases: rectangular Hardy operator, bilinear inequality, weighted Lebesgue norm.

MSC: 26D10, 47G10

Received: 02.06.2023

Language: English

DOI: 10.32523/2077-9879-2023-14-4-47-62


© Steklov Math. Inst. of RAS, 2024