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arXiv · 2204.05099

Oscillation estimates for truncated singular Radon operators

Wojciech Słomian
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Abstract

In this paper we prove uniform oscillation estimates on $L^p$, with $p\in(1,\infty)$, for truncated singular integrals of the Radon type associated with Calder\'on-Zygmund kernel, both in continuous and discrete settings. In the discrete case we use the Ionescu-Wainger multiplier theorem and the Rademacher-Menshov inequality to handle the number-theoretic nature of the discrete singular integral. The result we obtained in the continuous setting can be seen as a generalisation of the results of Campbell, Jones, Reinhold and Wierdl for the continuous singular integrals of the Calder\'on-Zygmund type.

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Wojciech Słomian. 2022-04-11. Oscillation estimates for truncated singular Radon operators. https://doi.org/10.1007/s00041-022-09986-8

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