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In this article we apply the uniform and \(L_{p}\) , \(1\leq p<\infty \) approximation properties of general smooth multivariate singular integral operators over \(\mathbb {R}^{N}\) , \(N\geq 1\) . It is a trigonometric based approach with detailed applications to the corresponding smooth multivariate Poisson-Cauchy singular integral operators. The results are quantitative via Jackson type inequalities involving the first uniform and \(L_{p}\) moduli of continuity.

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Trigonometric Background Multivariate Smooth Poisson-Cauchy Singular Integrals Approximation

  • 会议论文

  • 发表日期：

    2026年

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  • George A. Anastassiou

摘要

In this article we apply the uniform and \(L_{p}\) , \(1\leq p<\infty \) approximation properties of general smooth multivariate singular integral operators over \(\mathbb {R}^{N}\) , \(N\geq 1\) . It is a trigonometric based approach with detailed applications to the corresponding smooth multivariate Poisson-Cauchy singular integral operators. The results are quantitative via Jackson type inequalities involving the first uniform and \(L_{p}\) moduli of continuity.