6 papers · 1 filter
Generalised Hajłasz-Besov spaces on -spaces
Joaquim Martin, Walter A. Ortiz
An space is a doubling measure metric space with the additional property that it has a reverse doubling property. In this paper we introduce a new class of Hajłasz-Besov s…
A note on rearrangement Poincaré inequalities and the doubling condition
Joaquim Martín, Walter A. Ortiz
We introduce Poincaré type inequalities based on rearrangement invariant spaces in the setting of metric measure spaces and analyze when they imply the doubling condition on the un…
Non-collapsing condition and Sobolev embeddings for Hajłasz-Besov spaces
Joaquim Martin, Walter A. Ortiz
In this paper we will focus on understanding the relation between Sobolev embedding theorems for Hajłasz-Besov spaces defined on a doubling metric measure space and the n…
Sobolev embeddings for Fractional Hajłasz-Sobolev spaces in the setting of rearrangement invariant spaces
Joaquim Martin, Walter A. Ortiz
We obtain symmetrization inequalities in the context of Fractional Hajlasz-Sobolev spaces in the setting of rearrangement invariant spaces and prove that for a large class of measu…
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…
A density result on Orlicz-Sobolev spaces in the plane
Walter A. Ortiz, Tapio Rajala
We show the density of smooth Sobolev functions in the Orlicz-Sobolev spaces for bounded simply connected planar domains and doub…