Irene Drelichman

Improved Poincaré inequalities with weights

Abstract In this paper we prove that if Ω ∈ R n is a bounded John domain, the following weighted Poincare-type inequality holds: inf a ∈ R ‖ f ( x ) − a ‖ L q ( Ω , w 1 ) ⩽ C ‖ ∇ f ( x ) d ( x ) α ‖ L p ( Ω , w 2 ) where f is a locally Lipschitz function on Ω, d ( x ) denotes the distance of x to the boundary of Ω, the weights w 1 , w 2 satisfy certain cube conditions, and α ∈ [ 0 , 1 ] depends on p , q and n. This result generalizes previously known weighted inequalities, which can also be obtained with our approach.

Elementary Proofs of Embedding Theorems for Potential Spaces of Radial Functions

We present elementary proofs of weighted embedding theorems for radial potential spaces and some generalizations of Ni’s and Strauss’ inequalities in this setting.

Radial Solutions for Hamiltonian Elliptic Systems With Weights

Abstract We prove the existence of infinitely many radial solutions for elliptic systems in ℝn with power weights. A key tool for the proof will be a weighted imbedding theorem for fractional-order Sobolev spaces, that could be of independent interest.

Weighted inequalities for the fractional Laplacian and the existence of extremals

In this article we obtain improved versions of Stein-Weiss and Caffarelli-Kohn-Nirenberg inequalities, involving Besov norms of negative smoothness. As an application of the former, we derive the existence of extremals of the Stein-Weiss inequality in certain cases, some of which are not contained in the celebrated theorem of E. Lieb.