MAXIMAL OPERATORS OF THE FEJÉR MEANS OF THE TWO DIMENSIONAL CHARACTER SYSTEM OF THE p-SERIES FIELD IN THE KACZMARZ REARRANGEMENT
نویسنده
چکیده
The main aim of this paper is to prove that the maximal operator σ∗ of the Fejér means of the two dimensional character system of the p-series field in the Kaczmarz rearrangement is bounded from the Hardy space Hα to the space Lα for α > 1/2, provided that the supremum in the maximal operator is taken over a positive cone. We also prove that the maximal operator σ∗ 0 of Fejér means of the two dimensional character system of the p-series field in the Kaczmarz rearrangement is not bounded from the Hardy space H1/2 to the space weak-L1/2.
منابع مشابه
TWO–PARAMETER SUNOUCHI OPERATOR WITH RESPECT TO CHARACTER SYSTEM OF p–SERIES FIELD IN THE KACZMARZ REARRANGEMENT
Let Gp be p -series field. We prove the restricted two-parameter Sunouchi operator T χ h is bounded from H q to Lq for 0 < q 1 . By means of interpolation and duality argument, this theorem can be extended to Hardy-Lorentz spaces. As a consequence, we prove the restricted Sunouchi operator is of weak type (L1,L1) . Mathematics subject classification (2010): 42C10.
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