On the Rate of Almost Everywhere Convergence of Certain Classical Integral Means

Alexander M. Stokolos; Walter Trebels

doi:10.1006/jath.1998.3285

On the Rate of Almost Everywhere Convergence of Certain Classical Integral Means

Alexander M. Stokolos, Walter Trebels

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

The main purpose of this article is to establish nearly optimal results concerning the rate of almost everywhere convergence of the Gauss-Weierstrass, Abel-Poisson, and Bochner-Riesz means of the one-dimensional Fourier integral. A typical result for these means is the following: If the function f belongs to the Besov spaceB^s_p,p, 1<p<∞, 0<s<1, thenT_mtf (x)-f(x)=o_x(t^s) a.e. ast→0+.

Original language	English
Pages (from-to)	203-222
Number of pages	20
Journal	Journal of Approximation Theory
Volume	98
Issue number	2
DOIs	https://doi.org/10.1006/jath.1998.3285
State	Published - Jun 1999

Scopus Subject Areas

Analysis
Numerical Analysis
General Mathematics
Applied Mathematics

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10.1006/jath.1998.3285

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title = "On the Rate of Almost Everywhere Convergence of Certain Classical Integral Means",

abstract = "The main purpose of this article is to establish nearly optimal results concerning the rate of almost everywhere convergence of the Gauss-Weierstrass, Abel-Poisson, and Bochner-Riesz means of the one-dimensional Fourier integral. A typical result for these means is the following: If the function f belongs to the Besov spaceBsp,p, 1mtf (x)-f(x)=ox(ts) a.e. ast→0+.",

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AU - Trebels, Walter

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AB - The main purpose of this article is to establish nearly optimal results concerning the rate of almost everywhere convergence of the Gauss-Weierstrass, Abel-Poisson, and Bochner-Riesz means of the one-dimensional Fourier integral. A typical result for these means is the following: If the function f belongs to the Besov spaceBsp,p, 1mtf (x)-f(x)=ox(ts) a.e. ast→0+.

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DO - 10.1006/jath.1998.3285

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On the Rate of Almost Everywhere Convergence of Certain Classical Integral Means

Abstract

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