kaz29Вестник Казахстанско-Британского технического университетаHerald of the Kazakh-British Technical University1998-66882959-8109Казахстанско-Британский Технический Университет10.55452/1998-6688-2025-22-2-220-241kaz29-2003Research ArticleМАТЕМАТИЧЕСКИЕ НАУКИMATHEMATICAL SCIENCESТРЕХВЕСОВЫЕ НЕРАВЕНСТВА ДЛЯ НЕКОТОРОГО КЛАССА МАТРИЧНЫХ ОПЕРАТОРОВTHREE-WEIGHTED INEQUALITIES FOR SOME CLASS OF MATRIX OPERATORShttps://orcid.org/0000-0003-0402-6999ЖаңабергеноваН. С.ZhangabergenovaN. S.

PhD 

г. Астана 

 PhD 

 Astana 

zhanabergenova.ns@gmail.comhttps://orcid.org/0000-0001-5610-3314ТемирхановаА. Т.TemirhanovaA. T.

 PhD 

 г. Астана 

 PhD 

 Astana 

ainura-t@yandex.kzЕвразийский национальный университет им. Л.Н. ГумилеваКазахстанL.N. Gumilyov Eurasian National UniversityKazakhstan202506072025222220241Copyright © Жаңабергенова Н.С., Темирханова А.Т., 20252025Жаңабергенова Н.С., Темирханова А.Т.Zhangabergenova N.S., Temirhanova A.T.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnik.kbtu.edu.kz/jour/article/view/2003

Критерии выполнения непрерывных и дискретных неравенств, включающих операторы Харди, являются одной из ключевых проблем в теории весовых неравенств. Рассмотрение дискретных неравенств для класса матричных операторов можно считать новым направлением исследований. В общем случае, поскольку критерий устойчивости в весовом пространстве Лебега для дискретного оператора с матричным ядром не определен, к матрице задаются различные условия, что позволяет получать более широкие результаты по сравнению со случаем без матрицы. В данной работе мы рассматриваем дискретные квазилинейные операторы с матрицами, удовлетворяющими определенным условиям. Полученные результаты для квазилинейных неравенств могут быть применены при описании билинейных неравенств Харди.

The criteria for the fulfillment of continuous and discrete inequalities involving Hardy operators are one of the key problems in the theory of weighted inequalities. The study of discrete inequalities for the class of matrix operators can be considered a new direction of research. In general, since the stability criterion in the weighted Lebesgue space for a discrete operator with a matrix kernel is not defined, various conditions are imposed on the matrix, which allows for obtaining broader results compared to the case without a matrix. In this work, we consider discrete quasilinear operators with matrices satisfying certain conditions. The results obtained for quasilinear inequalities can be applied to the description of bilinear Hardy inequalities.

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The authors declare that there are no conflicts of interest present.