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Riesz Type Kernels over the Ring of Integers of a Local Field

โœ Scribed by Shijun Zheng

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
325 KB
Volume
208
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

Let O denote the ring of integers of a local field. In this note we prove an ร„ 4 ฯฑ approximation theorem for the Riesz type kernels โฅ over O. The proof , , n ns1 ลฝ . 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 solve the local field analog of ลฝ . N. J. Fine's problem Trans. Amer. Math. Soc. 65, 1949, 372แŽ414 concerning rates of convergence of the Fejer sum on the Walsh system. Our approach has potential รกpplications to other operators such as Cesaro means and AbelแŽPoisson means of ''type I.'' แฎŠ 1997 Academic Press

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