Abstract
We give a new Hilbert-type integral inequality with the best constant factor by estimating the weight function. And the equivalent form is considered.
Highlights
If f,g are real functions such that 0 < ∞ 0 f 2(x) dx < ∞ and ∞ 0 g 2 (x)dx∞, we have ∞ 0(x)g ( y ) x+y dx d y
Now we study the following inequality
Then by (2.5), we find 0 < g2(y)d y
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Summary
Introduction
We give a new Hilbert-type integral inequality with the best constant factor by estimating the weight function. Inequality (1.1) had been generalized by Hardy in 1925 as follows. Where the constant factor π/ sin(π/ p) is the best possible.
Results
Conclusion
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