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arXiv · 1702.05975

On square functions with independent increments and Sobolev spaces on the line

Julià Cufí·Artur Nicolau·Andreas Seeger·Joan Verdera
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Abstract

We prove a characterization of some $L^p$-Sobolev spaces involving the quadratic symmetrization of the Calder\'on 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 $\dot H^1_\alpha$. We also use a local version of this square function to characterize pointwise differentiability for functions in the Zygmund class.

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Julià Cufí, Artur Nicolau, Andreas Seeger, Joan Verdera. 2017-02-20. On square functions with independent increments and Sobolev spaces on the line. https://arxiv.org/abs/1702.05975

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