Maximal Operators of the Fejér means of the two dimensional character system of the p-series field in the Kaczmarz rearrangement U. Goginava Received: November 15, 2007; Accepted: April 25, 2008 Abstract. The main aim of this paper is to prove that the maximal operator σ* of the Fejéer 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 proved that the maximal operator σ0* 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 . Keywords: Character system, Weak type inequality. AMS Subject classification: Primary: 42C10 Version to read: PDF ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2008, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |