2 citations · 6 across the 5 of their papers we have counts for
5 papers
Approximation by mappings with singular Hessian minors
Zhuomin Liu, Jan Malý, Mohammad Reza Pakzad
Let be a Lipschitz domain. Given and any belonging to the little Hölder class , we construct a sequence in…
A Marcinkiewicz integral type characterization of the Sobolev space
Piotr Hajłasz, Zhuomin Liu
In this paper we present a new characterization of the Sobolev space , which is a higher dimensional version of a result of Waterman. We also provide a new an…
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…
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…
Rigidity and regularity of co-dimension one Sobolev isometric immersions
Zhuomin Liu, Mohammad Reza Pakzad
We prove the developability and regularity of isometric immersions of -dimensional domains into . As a conclusion we show that any such Sobolev is…