© 2017, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany. We prove a characterization of some Lp-Sobolev spaces involving the quadratic symmetrization of the Calderón commutator kernel, which is related to a square function with differences of difference quotients. An endpoint weak type estimate is established for functions in homogeneous Hardy–Sobolev spaces H˙α1. We also use a local version of this square function to characterize pointwise differentiability for functions in the Zygmund class.
|Journal||Annali di Matematica Pura ed Applicata|
|Publication status||Published - 1 Jun 2018|
- Hardy space
- Sobolev space
- Square function
- Zygmund class