Some jump and variational inequalities for the Calderón commutators and related operators
arXiv:1709.03127
Abstract
In this paper, we establish jump and variational inequalities for the Calderón commutators, which are typical examples of non-convolution Calderón-Zygmund operators. For this purpose, we also show jump and variational inequalities for para-products and commutators from pseudo-differential calculus, which are of independent interest. New ingredients in the proofs involve identifying Carleson measures constructed from sequences of stopping times, in addition to many Littlewood-Paley type estimates with gradient.
44 pages