We establish an analog Hardy inequality with sharp constant involving exponential weight function. The special case of this inequality (for n = 2) leads to a direct proof of Onofri inequality on S.

We generalize a Hardy-Littlewood inequality and a Privalov inequality for conjugate harmonic functions in the plane to components of Clifford-valued monogenic functions.

An inequality of Hardy type is established for quadratic forms involving Dirac operator and a weight r for functions in R. The exact Hardy constant cb = cb(n) is found and generalized minimizers are given. The constant cb vanishes on a countable set of b, which extends the known case n = 2, b = 0 which corresponds to the trivial Hardy inequality in R. Analogous inequalities are proved in the ca...

This Ph.D. thesis deals with various generalizations of the inequalities by Carleman, Hardy and Pólya-Knopp. In Chapter 1 we give an introduction and overview of the area that serves as a frame for the rest of the thesis. In Chapter 2 we consider Carleman’s inequality, which may be regarded as a discrete version of Pólya-Knopp’s inequality and also as a natural limiting inequality of the discre...

There are at least two directions concerning the extension of classical sharp Hardy-Littlewood-Sobolev inequality: (1) Extending the sharp inequality on general manifolds; (2) Extending it for the negative exponent λ = n−α (that is for the case of α > n). In this paper we confirm the possibility for the extension along the first direction by establishing the sharp Hardy-Littlewood-Sobolev inequ...

In this paper we obtain an inequality on the unit disk B in R2, which improves the classical Moser-Trudinger inequality and the classical Hardy inequality at the same time. Namely, there exists a constant C0 > 0 such that ∫ B e 4πu2 H(u) dx ≤ C0 <∞, ∀ u ∈ C 0 (B), where H(u) := ∫

An impulsive Cohen-Grossberg neural network with time-varying and S-type distributed delays and reaction-diffusion terms is considered. By using Hardy-Poincaré inequality instead of Hardy-Sobolev inequality or just the nonpositivity of the reaction-diffusion operators, under suitable conditions in terms of M-matrices which involve the reaction-diffusion coefficients and the dimension and size o...

By the method of weight coefficients, techniques of real analysis and Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality related to the kernel of the hyperbolic cosecant function with the best possible constant factor expressed in terms of the extended Riemann-zeta function is proved. The more accurate equivalent forms, the operator expressions with the norm, the rever...

[1] G. H. HARDY, J. E. LITTLEWOOD AND G. POLYA, Inequalities, Cambridge Univ. Press, Cambridge, 1995. [2] GAO MINGZHE, A Note on the Hardy-Hilbert Inequality, J. Math. Anal. Appl. Vol. 204, No. 1 (1996), 346–351. [3] GAO MINGZHE AND YANG BICHEN, on the Extended Hilbert’s Inequality, Proc. Amer. Math. Soc. Vol. 126, No. 3 (1998), 751–759. [4] W. H. GREUB, Linear Algebra, Springer Verlag, Berlin,...

In the present paper, by introducing some parameters, new forms of Hardy-Hilbert’s inequalities are given.