不同性质加权大洛伦兹空间上的乘法算子

Q3 Mathematics

WSEAS Transactions on Mathematics Pub Date : 2023-05-04 DOI:10.37394/23206.2023.22.32

I. Eryilmaz

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引用次数: 0

摘要

将勒贝格空间的概念推广到具有非权和权的大勒贝格空间，将经典洛伦兹空间的概念推广到具有类似逻辑的大洛伦兹空间。本文采用极大函数1<=p, q<=∞来定义加权大洛伦兹空间，而不是对可测函数进行重排，其中权函数是可测的、复值的、局部有界的。此外，定义了加权大洛伦兹空间上的乘法算子，并刻画了这些算子的有界性、闭值域、可逆性、紧性和封闭性等基本性质。

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Multiplication Operators on Weighted Grand Lorentz Spaces with Various Properties

The concept of Lebesgue space has been generalized to the grand Lebesgue space with non-weight and weight, and the classical Lorentz space concept has been generalized to grand Lorentz spaces with a similar logic. In this study, instead of using rearrangement for a measurable function, weighted Grand Lorentz spaces are defined by using the maximal function 1<=p, q<=∞ where the weight function is measurable, complex valued, and locally bounded. In addition, multiplication operators on weighted grand Lorentz spaces are defined and the fundamental properties of these operators such as boundedness, closed range, invertibility, compactness, and closedness are characterized.

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来源期刊

WSEAS Transactions on Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： WSEAS Transactions on Mathematics publishes original research papers relating to applied and theoretical mathematics. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with linear algebra, numerical analysis, differential equations, statistics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.