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

洪勇, 赵茜

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

HONG Yong, ZHAO Qian

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 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

Abstract: 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.

Key words: Weighted Lebesgue space, Weighted normed sequence space, Semi-discrete Hilbert-type inequalities, Integral operator, Discrete operator, Bounded operator, Opera-tor 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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[2]	洪勇, 冯明军. 序列空间l和函数空间 L 之间具有齐次核的 Hilbert 型算子有界的参数条件 [J]. 数学季刊, 2022, 37(1): 94-102.
[3]	洪勇, 和炳. 具有非齐次核的半离散 Hilbert 型多重积分不等式的最佳搭配参数及其应用 [J]. 数学季刊, 2021, 36(3): 252-262.
[4]	金建军, 李春华. 经典Hilbert不等式的p进制版本[J]. 数学季刊, 2020, 35(4): 431-440.
[5]	熊良鹏. 算子化单叶解析函数的优化结果和系数边界[J]. 数学季刊, 2017, 32(2): 142-151.
[6]	马丽娜 , 李书海. 由广义Dziok-Srivastava算子及其积分算子定义的亚纯多叶倒星象函数的某些新子类[J]. 数学季刊, 2015, 30(4): 532-544.
[7]	李书海, 马丽娜, 敖恩. 关于复阶k一致α-凸p叶函数类的新积分算子的凸性[J]. 数学季刊, 2014, 29(1): 88-96.
[8]	周娟, 朱月萍. 非双倍测度下多线性奇异积分算子及其交换子在Morrey-Herz型空间上的有界性[J]. 数学季刊, 2012, 27(4): 545-555.
[9]	鲁大前, 刘金林. 一类算子的凸性条件[J]. 数学季刊, 2011, 26(2): 185-189.
[10]	李宗涛, 刘名生. 某个用Carlson-Shaffer算子定义的解析函数子类的性质[J]. 数学季刊, 2011, 26(2): 245-250.
[11]	郭健, 刘永民. 从B⁰到Q_K和Q_K,0空间的复合算子[J]. 数学季刊, 2010, 25(1): 86-91.
[12]	喻德坚. 具广义周期边界条件之含第一类界参数抽象动力方程边值问题的积分算子求解法[J]. 数学季刊, 2010, 25(1): 110-117.
[13]	赵凯, 王磊. 一类振荡奇异积分算子的有界性[J]. 数学季刊, 2009, 24(4): 598-604.
[14]	刘永民. 映入 E(p,q)的复合算子[J]. 数学季刊, 2003, 18(1): 29-34.

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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