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On the Cesàro Means of Conjugate Jacobi Series

✍ Scribed by Zhongkai Li

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
283 KB
Volume
91
Category
Article
ISSN
0021-9045

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✦ Synopsis

This paper deals with the CesaÁ ro means of conjugate Jacobi series introduced by Muckenhoupt and Stein and Li. The exact estimates of the norms of the conjugate (C, $) kernel for 0 $ :+ 1 2 are obtained. It is proved that when $>:+ 1 2 , the (C, $) means of the conjugate Jacobi expansion of a function f converges almost everywhere to its (Jacobi) conjugate function and so does the (C, :+ 1

2 ) means at the critical index under the criterius of Lebesgue type by use of the equiconvergence theorem.

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Cesàro Summability of Hardy Spaces on th
Cesàro Summability of Hardy Spaces on the Ring of Integers in a Local Field
✍ Shijun Zheng 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 181 KB

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?