86 citations · 185 across the 36 of their papers we have counts for
4 papers · 1 filter
Norms supporting the Lebesgue differentiation theorem
Paola Cavaliere, Andrea Cianchi, Luboš Pick +1
A version of the Lebesgue differentiation theorem is offered, where the norm is replaced with any rearrangement-invariant norm. Necessary and sufficient conditions for a norm…
Banach algebras of weakly differentiable functions
Andrea Cianchi, Luboš Pick, Lenka Slavíková
The question is addressed of when a Sobolev type space, built upon a general rearrangement-invariant norm, on an -dimensional domain, is a Banach algebra under pointwise multipl…
Pointwise Calderón-Zygmund gradient estimates for the -Laplace system
Dominic Breit, Andrea Cianchi, Lars Diening +2
Pointwise estimates for the gradient of solutions to the -Laplace system with right-hand side in divergence form are established. They enable us to develop a nonlinear counterpa…
Sobolev inequalities in arbitrary domains
Andrea Cianchi, Vladimir Maz'ya
A theory of Sobolev inequalities in arbitrary open sets of Euclidean space is established. Boundary regularity of domains is replaced with information on boundary traces of trial f…