Abstract
By introducing two pairs of conjugate exponents and estimating the weight coefficients, we establish reverse versions of Hilbert-type inequalities, as described by Jin (J. Math. Anal. Appl. 340:932-942, 2008), and we prove that the constant factors are the best possible. As applications, some particular results are considered.
Highlights
If both an and bn ≥, such that < ∞ n= a n < ∞ and b n ∞, we have∞ ∞ ambn < π m+n b n, n= m= n= ( . )where the constant factor π has the best possible value
Hardy-Hilbert inequality, which is important in analysis and applications
It is easy to show that the above inequalities take the form of a strict inequality
Summary
Where the constant factor π has the best possible value. ) has been generalized by Hardy as follows. Where the constant factor π sin(π /p) is the best possible. Hardy-Hilbert inequality, which is important in analysis and applications (see [ ]). Many results with generalizations of this type of inequality have been obtained (see [ ]). ), there are some Hilbert-type inequalities that are similar to By studying a Hilbert-type operator, Jin [ ] obtained a new bilinear operator inequality with the norm, and he provided some new Hilbert-type inequalities with the best constant factor. Reduces to Yang’s result [ ] as follows. Where the constant factors kp and (kp)p are the best possible.
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