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On Hardy-Bessel potential spaces over the ring of integers in a local field

✍ Scribed by Jun Tateoka


Book ID
112650890
Publisher
Springer
Year
1994
Tongue
English
Weight
402 KB
Volume
20
Category
Article
ISSN
0133-3852

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## Abstract The purpose of this paper is to present characterizations of the inhomogeneous Hardy‐Bessel potential spaces __F^p^__~α~ (__K__) over the 2‐series field __K__ defined by Littlewood‐Paley type function, magnified image where Δ~0~(__x__) = 1(|x|≥1), = 0(other), Δ~__j__~(__x__) = 2^__j__^

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Let O denote the ring of integers of a local field. In this note we prove an Ä 4 ϱ approximation theorem for the Riesz type kernels ␥ over O. The proof , , n ns1 Ž . y1 requires a sharp estimate of the Dirichlet kernel D x on P \_ O, which may also n have independent interest. As a consequence we so