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.

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) := ∫

In this article we derive a generalized version of nonlinear Picone’s identity for the p-Laplacian. We use this identity to obtain a Hardy-type inequality and a Sturm comparison result. We also establish the relationship between the components of the solution of nonlinear elliptic systems.

We prove an existence and uniqueness result for ground states and for purely angular excitations of two-dimensional Schrödinger-Newton equations. From the minimization problem for ground states we obtain a sharp version of a logarithmic Hardy-Littlewood-Sobolev type inequality.

Let Md be the centered Hardy-Littlewood maximal function associated to cubes in R with Lebesgue measure, and let cd denote the lowest constant appearing in the weak type (1,1) inequality satisfied by Md. We show that cd → ∞ as d → ∞, thus answering, for the case of cubes, a long standing open question of E. M. Stein and J. O. Strömberg.