18 citations · 62 across the 31 of their papers we have counts for
6 papers · 1 filter
Weak contact equations for mappings into Heisenberg groups
Zoltán M. Balogh, Piotr Hajłasz, Kevin Wildrick
Let k>n be positive integers. We consider mappings from a subset of k-dimensional Euclidean space R^k to the Heisenberg group H^n with a variety of metric properties, each of which…
Sobolev spaces, Lebesgue points and maximal functions
Piotr Hajlasz, Zhuomin Liu
In this note we study boundedness of a large class of maximal operators in Sobolev spaces that includes the spherical maximal operator. We also study the size of the set of Lebesgu…
Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces
Piotr Hajlasz, Armin Schikorra
We construct a smooth compact n-dimensional manifold Y with one point singularity such that all its Lipschitz homotopy groups are trivial, but Lipschitz mappings Lip(S^n,Y) are not…
Maximal potentials, maximal singular integrals, and the spherical maximal function
Piotr Hajlasz, Zhuomin Liu
We introduce a notion of maximal potentials and we prove that they form bounded operators from to the homogeneous Sobolev space for all . We appl…
The Lusin theorem and horizontal graphs in the Heisenberg group
Piotr Hajlasz, Jacob Mirra
In this paper we prove that every collection of measurable functions , coincides a.e. with th order derivatives of a function whose derivatives of or…
Homotopy groups of spheres and Lipschitz homotopy groups of Heisenberg groups
Piotr Hajlasz, Armin Schikorra, Jeremy T. Tyson
We provide a sufficient condition for the nontriviality of the Lipschitz homotopy group of the Heisenberg group, , in terms of properties of the classical homotopy…