Abstract
In this paper we introduce some new forms of the Hilbert integral inequality, and we study the connection between the obtained inequalities with Hardy inequalities. The reverse form and some applications are also given. MSC:26D15.
Highlights
The famous Hardy-Hilbert inequality for positive functions f, g and two conjugate parameters p and q such that p > + q = is given as ∞ ∞ f (x)g(y) π x+y dx dy < sin( π p
In [ ](see [ ]), the following Hardy-type inequality is obtained for p > :
For details about inequality ( . ) and its history and development, we refer the reader to the papers [ ] and [ ]
Summary
The famous Hardy-Hilbert inequality for positive functions f , g and two conjugate parameters p and q such that p. In [ ] the authors obtained the following extension of XpqA – f p(x) dx ypqA – gq(x) dx , where B( – pA , λ + pA – ) is the best possible constant (B(x, y) is the beta function), λ >. In [ ] the following extension was given: bb f (x)g(y). ). The following inequalities are special cases of Refinements of some Hilbert-type inequalities by virtue of various methods were obtained in [ , ] and [ ].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
