Trigonometric Induced Multivariate Smooth Gauss–Weierstrass Singular Integrals Approximation

George A. Anastassiou ()
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George A. Anastassiou: Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA

Mathematics, 2023, vol. 12, issue 1, 1-18

Abstract: In this article, we employ the uniform and L p , 1 ≤ p < ∞ approximation properties of general smooth multivariate singular integral operators over R N , N ≥ 1 . It is a trigonometric relief approach with detailed applications to the corresponding smooth multivariate Gauss–Weierstrass singular integral operators. The results are quantitative via Jackson-type inequalities involving the first uniform and L p moduli of continuity.

Keywords: multivariate singular integral operator; multivariate modulus of continuity; multivariate Gauss–Weierstrass operator; uniform and L p approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2023:i:1:p:115-:d:1309679

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