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

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

数学季刊 ›› 2024, Vol. 39 ›› Issue (1): 59-67.doi: 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

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

收稿日期:2022-07-08 出版日期:2024-03-30 发布日期:2024-03-13
通讯作者: HONG Yong (1959-), male, native of Guangzhou, Guangdong, professor of Guangzhou Huashang College, engages in harmonic analysis and analytical inequalities. E-mail: hongyonggdcc@yeah.net
作者简介: HONG Yong (1959-), male, native of Guangzhou, Guangdong, professor of Guangzhou Huashang College, engages in harmonic analysis and analytical inequalities.
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).

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

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

Received:2022-07-08 Online:2024-03-30 Published:2024-03-13
Contact: HONG Yong (1959-), male, native of Guangzhou, Guangdong, professor of Guangzhou Huashang College, engages in harmonic analysis and analytical inequalities. E-mail: hongyonggdcc@yeah.net
About author: HONG Yong (1959-), male, native of Guangzhou, Guangdong, professor of Guangzhou Huashang College, engages in harmonic analysis and analytical inequalities.
Supported by:
Supported by Guangdong Basic and Applied Basic Research Foundation (Grant No.
2022A1515012429); Guangzhou Huashang College Research Team Project (Grant No. 2021HSKT03).

摘要/Abstract

摘要： Using the weight coefficient method, we first discuss semi-discrete Hilberttype 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, Operator norm

Abstract: Using the weight coefficient method, we first discuss semi-discrete Hilberttype 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.

Key words: Weighted Lebesgue space, Weighted normed sequence space, Semi-discrete
Hilbert-type inequalities, Integral operator, Discrete operator, Bounded operator, Operator norm

中图分类号:

O178

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.

HONG Yong, ZHAO Qian. Boundedness of Integral and Discrete Operators Between Two Types of Weighted Spaces and Estimation of Operator Norm[J]. Chinese Quarterly Journal of Mathematics, 2024, 39(1): 59-67.

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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

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

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