Let n ≥ 2 and let A : Rn → [0,∞] be any convex function satisfying the following properties: A(0) = 0 and A(ξ) = A(−ξ) for ξ ∈ R; (1.1) for every t > 0, {ξ ∈ R : A(ξ) ≤ t} (1.2) is a compact set… (More)

A priori estimates for solutions to homogeneous Neumann problems for uniformly elliptic equations in open subsets Ω of R are established, with data in the limiting space L(Ω), or, more generally, in… (More)

We prove a sharp pointwise estimate of the nonincreasing rearrangement of the fractional maximal function of f, M f, by an expression involving the nonincreasing rearrangement of f. This estimate is… (More)

Abstract: An affine Moser-Trudinger inequality, which is stronger than the Euclidean MoserTrudinger inequality, is established. In this new affine analytic inequality an affine energy of the gradient… (More)

A unified approach is presented for establishing a broad class of Cramér-Rao inequalities for the location parameter, including, as special cases, the original inequality of Cramér and Rao, as well… (More)

Quantitative versions of sharp estimates for the supremum of Sobolev functions in W 1,p(Rn), p > n, with remainder terms depending on the distance from the families of extremals, are established.

We deal with eigenvalue problems for the Laplacian on noncompact Riemannian manifolds M of finite volume. Sharp conditions ensuring L(M) and L∞(M) bounds for eigenfunctions are exhibited in terms of… (More)

Inequality (1.2) is classical and very well known. It has been the object of extensions and variants which can be found in a number of papers and monographs, including [AFLT], [Bae], [BBMP], [BH],… (More)

A new approach to boundary trace inequalities for Sobolev functions is presented, which reduces any trace inequality involving general rearrangement-invariant norms to an equivalent, considerably… (More)