Naslov
On Hilbert type inequalities

Autori
Pečarić, Josip ; Perić, Ivan ; Vuković, Predrag

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Skup
4th World Conference on 21st Century Mathematics 2009

Mjesto i datum
Lahore, Pakistan, 04.03.2009. - 08.03.2009

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Hardy-Hilbert's inequality; homogeneous kernel; the best possible constant; conjugate exponents; non-conjugate exponents; the hypergeometric fuction

Sažetak
In this talk we give some new generalizations of classical Hilbert's inequality. We extend it to a general case with $k\geq 2$ non-conjugate exponents. The established technique is then applied to the case where functions are defined $R^n$, and in the case of conjugate exponents and some special homogeneous kernels it is shown that the obtained inequalities are the best possible. A generalization of the Hilbert-Pachpatte inequality and refinements of the Hilbert inequality using the Laplace transform are also presented. The problem of the best possibility of the Hilbert inequality with a general homogeneous kernel is considered in the case where functions are defined on $R_{;+};$.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA