Cesăro summability of the character system of the p-series field in the Kaczmarz rearrangement |
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Authors: | György Gát Károly Nagy |
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Institution: | (1) Department of Mathematics, Bessenyei College, Nyíregyháza, P.O.Box 166, H-4400, Hungary E-mail;(2) Department of Mathematics, Bessenyei College, Nyíregyháza, P.O.Box 166, H-4400, Hungary E-mail |
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Abstract: | Let $G_p$ be the $p$-series field. In this paper we prove the a.e. convergence $\sigma_n f\to f$ $(n\to \infty)$ for an integrable function $f\in L^1(G_p)$, where $\sigma_nf$ is the $n$th $(C,1)$ mean of $f$ with respect to the character system in the Kaczmarz rearrangement. We define the maximal operator $\sigma^* $ by $\sigma^*f := \sup_n|\sigma_nf|$. We prove that $\sigma^*$ is of type $(q,q)$ for all $1
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