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

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arxiv 1702.05975 v2 pith:YZQA4RM5 submitted 2017-02-20 math.CA

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

classification math.CA
keywords functionsspacessquarefunctionsobolevalphacaldercharacterization
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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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