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On Some Singular Integrals in Hölder Spaces

✍ Scribed by B. Firlejy; L. Rempulska

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
222 KB
Volume
170
Category
Article
ISSN
0025-584X

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✦ Synopsis

The approximation of functions by singular integrals is an important question in the theory of differential and integral equations. Therefore the consideration of approximation problems in various norms is useful.

Recently in many papers approximation problems have been studied in the Holder norms

In [2] the orders of approximation are obtained for the Picard, Poisson-Cauchy and GauD-WeierstraD singular integrals in the supremum norm and the classical Holder norm. In [3] error estimates for the Fourier sum and the trigonometric interpolatory polynomial are given in generalized Holder norms.

Using notations given in [2] and [3], we present in this paper approximation theorems for the singular integrals [2] in some generalized Holder norms. Those theorems contain and improve the results obtained in [2].

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