Oscillation estimates for truncated singular Radon operators

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 Calderón-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 Calderón-Zygmund type.

16 pages, no figures, accepted for publication in the Journal of Fourier Analysis and Applications

Cited by in corpus (2)

• Oscillation and jump inequalities for the polynomial ergodic averages along multi-dimensional subsets of primes
• Bootstrap methods in bounding discrete Radon operators