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arXiv · 1709.03127

Some jump and variational inequalities for the Calder\'on commutators and related operators

Yanping Chen·Yong Ding·Guixiang Hong·Jie Xiao
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Abstract

In this paper, we establish jump and variational inequalities for the Calder\'{o}n commutators, which are typical examples of non-convolution Calder\'on-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.

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Yanping Chen, Yong Ding, Guixiang Hong, Jie Xiao. 2017-09-10. Some jump and variational inequalities for the Calder\'on commutators and related operators. https://arxiv.org/abs/1709.03127

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