关键词: p级数域, Kaczmarz 重排法则, Hardy-Lorentz 空间

Abstract:

Let G_p be the p-series field. G.Gát and K.Nagy^[8] have shown that the maximal operator of the (C,1) means of the character system of the p-series filed in the Kaczmarz rearrangement is of type (q,q) for all 1<q ≤ ∞ and of weak type (1,1). In the present work the authors  extend these results to the (C, α) means where 0 < α ≤ 1 and prove
its maximal operator σ^~α: H^p → L^p is bounded for all 1/(α+1) < p ≤ 1. By means of interpolation and duality argument, this theorem can be extended to Hardy-Lorentz spaces. As a consequence, the $(C,\alpha)$ means of an integrable function f converge to f a.e..

Key words: p-series field, Kaczmarz rearrangement, Hardy-Lorentz space