49 citations · 140 across the 17 of their papers we have counts for
19 papers
Oscillation Classes: An Interpolation Approach
Joaquim Martin
Let \(φ\) be an admissible concave function on \((0,1)\) and let \(X\) be a rearrangement-invariant space. We study the classes determined by the oscillation functional \[ \mathcal…
Oscillation inequalities, lower ball growth and Sobolev embeddings on metric measure spaces
Joaquim Martín
We study the relation between lower ball growth, rearrangement oscillations, and Sobolev-type embeddings on metric measure spaces. We prove that a lower estimate for the ball funct…
Oscillation Functionals and Embeddings in Rearrangement-Invariant Spaces
Joaquim Martin
We study embeddings associated with oscillation functionals in rearrangement-invariant spaces. More precisely, given a positive function \(ψ\), we analyze how the interaction betwe…
Symmetrization Inequalities for Probability metric spaces with Convex Isoperimetric profile
Joaquim Martin, Walter A. Ortiz
We obtain symmetrization inequalities on probability metric spaces with convex isoperimetric profile which incorporate in their formulation the isoperimetric estimator and that can…
Isoperimetric weights and generalized uncertainty inequalities in metric measure spaces
Joaquim Martin, Mario Milman
We extend the recent uncertainty inequalities obtained by Dall'ara-Trevisan to the metric setting. For this purpose we introduce a new class of weights, named *isoperimetri…
Towards a unified theory of Sobolev inequalities
Joaquim Martin, Mario Milman
We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to un…