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arXiv · 1709.03123

Weighted jump and variational inequalities for rough operators

Yanping Chen·Yong Ding·Guixiang Hong·Honghai Liu
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Abstract

In this paper, we systematically study weighted jump and variational inequalities for rough operators. More precisely, we show some weighted jump and variational inequalities for the families $\mathcal T:=\{T_\varepsilon\}_{\varepsilon>0}$ of truncated singular integrals and $\mathcal M_{\Omega}:=\{M_{\Omega,t}\}_{t>0}$ of averaging operators with rough kernels, which are defined respectively by $$ T_\varepsilon f(x)=\int_{|y|>\varepsilon}\frac{\Omega(y')}{|y|^n}f(x-y)dy$$ and $$M_{\Omega,t} f(x)=\frac1{t^n}\int_{|y| 1$.

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Yanping Chen, Yong Ding, Guixiang Hong, Honghai Liu. 2017-09-10. Weighted jump and variational inequalities for rough operators. https://arxiv.org/abs/1709.03123

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