2023
DOI: 10.1186/s13660-023-02951-z
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A half-discrete Hilbert-type inequality in the whole plane with the constant factor related to a cotangent function

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 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… Show more

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