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- W4319725257 abstract "Abstract 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 non-homogeneous cases. By employing some techniques of real analysis, especially the way of 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. Lastly, assigning special values to the parameters, some new half-discrete Hilbert-type inequalities with special kernels are presented at the end of the paper. 2020 Mathematics Subject Classification: Primary 26D15, 26D10; Secondary 47B38." @default.
- W4319725257 created "2023-02-11" @default.
- W4319725257 creator A5062349341 @default.
- W4319725257 date "2023-02-09" @default.
- W4319725257 modified "2023-10-18" @default.
- W4319725257 title "A half-discrete Hilbert-type inequality in the whole plane with the constant factor related to cotangent function" @default.
- W4319725257 doi "https://doi.org/10.21203/rs.3.rs-2555978/v1" @default.
- W4319725257 hasPublicationYear "2023" @default.
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