Abstract
In this article we apply the uniform and \(L_{p}\), \(1\le p<\infty \) approximation properties of general smooth multivariate singular integral operators over \({\mathbb {R}}^{N}\), \(N\ge 1\). It is a trigonometric based approach with detailed applications to the corresponding smooth multivariate trigonometric 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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Anastassiou, G.A. Trigonometric background multivariate smooth trigonometric singular integrals approximations. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 61 (2024). https://doi.org/10.1007/s13398-024-01560-9
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DOI: https://doi.org/10.1007/s13398-024-01560-9
Keywords
- Multivariate singular integral operator
- Multivariate modulus of continuity
- Multivariate trigonometric operator
- Uniform and \(L_{p}\) approximation