Marcinkiewicz-Fejer means of double conjugate Walsh-Kaczmarz-Fourier series and Hardy spaces

Authors: USHANGI GOGINAVA, KAROLY NAGY

Abstract: In the present paper we prove that for any 0 < p \leq 2/3 there exists a martingale f in H_p such that the Marcinkiewicz-Fejér means of double conjugate Walsh-Kaczmarz-Fourier series of the martingale f is not uniformly bounded in the space L_p.

Keywords: Walsh-Kaczmarz system, Fejér means, Marcinkiewicz means, Martingale-Hardy space

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