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Cesàro Summability of Hardy Spaces on the Ring of Integers in a Local Field

✍ Scribed by Shijun Zheng

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
181 KB
Volume
249
Category
Article
ISSN
0022-247X

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✦ Synopsis

Let O O be the ring of integers in a local field K. We solve an open problem due Ž to M. H. Taibleson 1975, ''Math. Notes,'' Vol. 15, Princeton Univ. Press, Prince-. 1 Ž . ton, NJ : Suppose f g L O O . Does the Cesaro means of f converge to f almost `Ž p p .

everywhere if K has characteristic zero? To this end we study the H , L boundedness of the associated maximal operator U to get the corresponding interpolation result on Hardy᎐Lorentz spaces; in particular we obtain that U is Ž . of weak type 1, 1 . The proof mainly depends on certain estimates for the oscillatory Dirichlet kernels, which are refinements of those obtained earlier by the Ž .

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Riesz Type Kernels over the Ring of Inte
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✍ Shijun Zheng 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 325 KB

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