Walsh-Marcinkiewicz means and Hardy spaces

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1. [1] Blahota I., On a norm inequality with respect to Vilenkin-like systems, Acta Math. Hungar., 2000, 89(1–2), 15–27 http://dx.doi.org/10.1023/A:1026769207159 Zbl0973.42020
2. [2] Blahota I., Gát G., Goginava U., Maximal operators of Fejér means of Vilenkin-Fourier series, JIPAM. J. Inequal. Pure Appl. Math., 2006, 7(4), #149 Zbl1232.42024
3. [3] Blahota I., Gát G., Goginava U., Maximal operators of Fejér means of double Vilenkin-Fourier series, Colloq. Math., 2007, 107(2), 287–296 http://dx.doi.org/10.4064/cm107-2-8 Zbl1117.42006
4. [4] Fine N.J., Cesàro summability of Walsh-Fourier series, Proc. Nat. Acad. Sci. U.S.A., 1955, 41(8), 588–591 http://dx.doi.org/10.1073/pnas.41.8.588 Zbl0065.05303
5. [5] Fujii N., A maximal inequality for H 1-functions on the generalized Walsh-Paley group, Proc. Amer. Math. Soc., 1979, 77(1), 111–116 
6. [6] Gát G., Investigations of certain operators with respect to the Vilenkin system, Acta Math. Hungar., 1993, 61(1–2), 131–149 http://dx.doi.org/10.1007/BF01872107 
7. [7] Glukhov V.A., Summation of multiple Fourier series in multiplicative systems, Mat. Zametki, 1986, 39(5), 665–673 (in Russian) Zbl0607.42020
8. [8] Goginava U., The maximal operator of Marcinkiewicz-Fejér means of the d-dimensional Walsh-Fourier series, East J. Approx., 2006, 12(3), 295–302 
9. [9] Goginava U., Maximal operators of Fejér-Walsh means, Acta Sci. Math. (Szeged), 2008, 74(3–4), 615–624 Zbl1199.42127
10. [10] Goginava U., Weak type inequality for the maximal operator of the Marcinkiewicz-Fejér means of the twodimensional Walsh-Fourier series, J. Approx. Theory, 2008, 154(2), 161–180 http://dx.doi.org/10.1016/j.jat.2008.03.012 Zbl1183.42028
11. [11] Goginava U., The weak type inequality for the Walsh system, Studia Math., 2008, 185(1), 35–48 http://dx.doi.org/10.4064/sm185-1-2 Zbl1213.42098
12. [12] Goginava U., The martingale Hardy type inequality for Marcinkiewicz-Fejér means of two-dimensional conjugate Walsh-Fourier series, Acta Math. Sin. (Engl. Ser.), 2011, 27(10), 1949–1958 http://dx.doi.org/10.1007/s10114-011-9551-7 
13. [13] Nagy K., Some convergence properties of the Walsh-Kaczmarz system with respect to the Marcinkiewicz means, Rend. Circ. Mat. Palermo (2) Suppl., 2005, 76, 503–516 Zbl1214.42056
14. [14] Nagy K., On the maximal operator of Walsh-Marcinkiewicz means, Publ. Math. Debrecen., 2011, 78(3–4), 633–646 http://dx.doi.org/10.5486/PMD.2011.4829 Zbl1249.42013
15. [15] Pál J., Simon P., On a generalization of the concept of derivative, Acta Math. Acad. Sci. Hungar., 1977, 29(1–2), 155–164 http://dx.doi.org/10.1007/BF01896477 Zbl0345.42011
16. [16] Schipp F., Certain rearrangements of series in the Walsh system, Mat. Zametki, 1975, 18(2), 193–201 (in Russian) 
17. [17] Schipp F., Wade W.R., Simon P., Walsh Series, Adam Hilger, Bristol, 1990 
18. [18] Simon P., Investigations with respect to the Vilenkin system, Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 1985, 27, 87–101 Zbl0586.43001
19. [19] Simon P., Strong convergence of certain means with respect to the Walsh-Fourier series, Acta Math. Hungar., 1987, 49(3-4), 425–431 http://dx.doi.org/10.1007/BF01951006 
20. [20] Simon P., Cesaro summability with respect to two-parameter Walsh systems, Monatsh. Math., 2000, 131(4), 321–334 http://dx.doi.org/10.1007/s006050070004 Zbl0976.42014
21. [21] Simon P., Remarks on strong convergence with respect to the Walsh system, East J. Approx., 2000, 6, 261–276 Zbl1084.42513
22. [22] Tephnadze G., Fejér means of Vilenkin-Fourier series, Stud. Sci. Math. Hungar., 2012, 49(1), 79–90 Zbl1265.42099
23. [23] Tephnadze G., On the maximal operator of Vilenkin-Fejér means, Turkish J. Math., 2013, 37(2), 308–318 Zbl1278.42037
24. [24] Tephnadze G., On the maximal operators of Vilenkin-Fejér means on Hardy spaces, Math. Inequal. Appl., 2013, 16(1), 301–312 Zbl1263.42008
25. [25] Tephnadze G., Strong convergence theorems for Walsh-Fejér means, Acta Math. Hungar., 2014, 142(1), 244–259 http://dx.doi.org/10.1007/s10474-013-0361-5 Zbl1313.42086
26. [26] Tephnadze G., A note on the norm convergence of Vilenkin-Fejér means, Georgian Math. J. (in press) Zbl1303.42012
27. [27] Weisz F., Martingale Hardy Spaces and their Applications in Fourier Analysis, Lecture Notes in Math., 1568, Springer, Berlin, 1994 Zbl0796.60049
28. [28] Weisz F., Cesàro summability of one- and two-dimensional Walsh-Fourier series, Anal. Math., 1996, 22(3), 229–242 http://dx.doi.org/10.1007/BF02205221 Zbl0866.42020
29. [29] Weisz F., Hardy spaces and Cesàro means of two-dimensional Fourier series, In: Approximation Theory and Function Series, Budapest, August 21–25, 1995, Bolyai Soc. Math. Studies, 5, János Bolyai Mathematical Society, Budapest, 1996, 353–367 
30. [30] Weisz F., Convergence of double Walsh-Fourier series and Hardy spaces, Approx. Theory Appl. (N.S.), 2001, 17(2), 32–44 
31. [31] Weisz F., Summability of Multi-Dimensional Fourier series and Hardy Space, Math. Appl., 541, Kluwer, Dordrecht, 2002 http://dx.doi.org/10.1007/978-94-017-3183-6