Denseness of domains of differential operators in Sobolev spaces.
Difference of general integral means.
Differentiability from the representation formula and the Sobolev-Poincaré inequality
In the geometries of stratified groups, we provide differentiability theorems for both functions of bounded variation and Sobolev functions. Proofs are based on a systematic application of the Sobolev-Poincaré inequality and the so-called representation formula.
Direct and Reverse Gagliardo-Nirenberg Inequalities from Logarithmic Sobolev Inequalities
We investigate the connection between certain logarithmic Sobolev inequalities and generalizations of Gagliardo-Nirenberg inequalities. A similar connection holds between reverse logarithmic Sobolev inequalities and a new class of reverse Gagliardo-Nirenberg inequalities.
Discretization and anti-discretization of rearrangement-invariant norms.
Disuguaglianze di Sobolev nello spazio iperbolico bidimensionale
Double exponential integrability, Bessel potentials and embedding theorems
This paper is a continuation of [5] and provides necessary and sufficient conditions for double exponential integrability of the Bessel potential of functions from suitable (generalized) Lorentz-Zygmund spaces. These results are used to establish embedding theorems for Bessel potential spaces which extend Trudinger's result.