两类加权空间间的积分算子与离散算子的有界性及算子范数估计

洪勇, 赵茜

doi:10.13371/j.cnki.chin.q.j.m.2024.01.005

数学季刊 >

2024 , Vol. 39 >Issue 1: 59 - 67

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2024.01.005

两类加权空间间的积分算子与离散算子的有界性及算子范数估计

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School of Data Science, Guangzhou Huashang College, Guangzhou 511300, China

HONG Yong (1959-), male, native of Guangzhou, Guangdong, professor of Guangzhou Huashang College, engages in harmonic analysis and analytical inequalities.

收稿日期: 2022-07-08

网络出版日期: 2024-03-13

基金资助

Supported by Guangdong Basic and Applied Basic Research Foundation (Grant No. 2022A1515012429); Guangzhou Huashang College Research Team Project (Grant No. 2021HSKT03).

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Boundedness of Integral and Discrete Operators Between Two Types of Weighted Spaces and Estimation of Operator Norm

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School of Data Science, Guangzhou Huashang College, Guangzhou 511300, China

HONG Yong (1959-), male, native of Guangzhou, Guangdong, professor of Guangzhou Huashang College, engages in harmonic analysis and analytical inequalities.

Received date: 2022-07-08

Online published: 2024-03-13

Supported by

Supported by Guangdong Basic and Applied Basic Research Foundation (Grant No. 2022A1515012429); Guangzhou Huashang College Research Team Project (Grant No. 2021HSKT03).

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摘要

Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.

关键词： Weighted Lebesgue space; Weighted normed sequence space; Semi-discrete Hilbert-type inequalities; Integral operator; Discrete operator; Bounded operator; Opera-tor norm

本文引用格式

洪勇, 赵茜 . 两类加权空间间的积分算子与离散算子的有界性及算子范数估计[J]. 数学季刊, 2024 , 39(1) : 59 -67 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.005

Abstract

Key words： Weighted Lebesgue space; Weighted normed sequence space; Semi-discrete Hilbert-type inequalities; Integral operator; Discrete operator; Bounded operator; Opera-tor norm

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