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A half-discrete Hilbert-type inequality in the whole plane with the constant factor related to a cotangent function

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Bibliographic Details
Main Author: Minghui, You
Format: Book
Language:English
Published: Springer 2023
Subjects:
homogeneous
nonhomogeneous cases
Online Access:https://link.springer.com/article/10.1186/s13660-023-02951-z
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7531
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spelling oai:localhost:PNK-75312023-04-05T02:53:21Z A half-discrete Hilbert-type inequality in the whole plane with the constant factor related to a cotangent function Minghui, You homogeneous nonhomogeneous cases CC BY In this work, by the introduction of some parameters, a new half-discrete kernel function in the whole plane is defined, which involves both the homogeneous and the nonhomogeneous cases. By employing some techniques of real analysis, especially the method of a weight function, a new half-discrete Hilbert-type inequality with the new kernel function, as well as its equivalent Hardy-type inequalities are established. Moreover, it is proved that the constant factors of the newly obtained inequalities are the best possible. Finally, assigning special values to the parameters, some new half-discrete Hilbert-type inequalities with special kernels are presented at the end of the paper. 2023-04-05T02:53:21Z 2023-04-05T02:53:21Z 2023 Book https://link.springer.com/article/10.1186/s13660-023-02951-z https://dlib.phenikaa-uni.edu.vn/handle/PNK/7531 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic homogeneous
nonhomogeneous cases
spellingShingle homogeneous
nonhomogeneous cases
Minghui, You
A half-discrete Hilbert-type inequality in the whole plane with the constant factor related to a cotangent function
description CC BY
format Book
author Minghui, You
author_facet Minghui, You
author_sort Minghui, You
title A half-discrete Hilbert-type inequality in the whole plane with the constant factor related to a cotangent function
title_short A half-discrete Hilbert-type inequality in the whole plane with the constant factor related to a cotangent function
title_full A half-discrete Hilbert-type inequality in the whole plane with the constant factor related to a cotangent function
title_fullStr A half-discrete Hilbert-type inequality in the whole plane with the constant factor related to a cotangent function
title_full_unstemmed A half-discrete Hilbert-type inequality in the whole plane with the constant factor related to a cotangent function
title_sort half-discrete hilbert-type inequality in the whole plane with the constant factor related to a cotangent function
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1186/s13660-023-02951-z
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7531
_version_ 1762365499381907456
score 8.891145

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