PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2014 | 12 | 8 | 1214-1228
Tytuł artykułu

Walsh-Marcinkiewicz means and Hardy spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The main aim of this paper is to investigate the Walsh-Marcinkiewicz means on the Hardy space H p, when 0 < p < 2/3. We define a weighted maximal operator of Walsh-Marcinkiewicz means and establish some of its properties. With its aid we provide a necessary and sufficient condition for convergence of the Walsh-Marcinkiewicz means in terms of modulus of continuity on the Hardy space H p, and prove a strong convergence theorem for the Walsh-Marcinkiewicz means.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
8
Strony
1214-1228
Opis fizyczny
Daty
wydano
2014-08-01
online
2014-05-08
Twórcy
Bibliografia
  • [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
  • [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
  • [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
  • [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
  • [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] 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] Glukhov V.A., Summation of multiple Fourier series in multiplicative systems, Mat. Zametki, 1986, 39(5), 665–673 (in Russian)
  • [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] Goginava U., Maximal operators of Fejér-Walsh means, Acta Sci. Math. (Szeged), 2008, 74(3–4), 615–624
  • [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
  • [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
  • [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] 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
  • [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
  • [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
  • [16] Schipp F., Certain rearrangements of series in the Walsh system, Mat. Zametki, 1975, 18(2), 193–201 (in Russian)
  • [17] Schipp F., Wade W.R., Simon P., Walsh Series, Adam Hilger, Bristol, 1990
  • [18] Simon P., Investigations with respect to the Vilenkin system, Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 1985, 27, 87–101
  • [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] 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
  • [21] Simon P., Remarks on strong convergence with respect to the Walsh system, East J. Approx., 2000, 6, 261–276
  • [22] Tephnadze G., Fejér means of Vilenkin-Fourier series, Stud. Sci. Math. Hungar., 2012, 49(1), 79–90
  • [23] Tephnadze G., On the maximal operator of Vilenkin-Fejér means, Turkish J. Math., 2013, 37(2), 308–318
  • [24] Tephnadze G., On the maximal operators of Vilenkin-Fejér means on Hardy spaces, Math. Inequal. Appl., 2013, 16(1), 301–312
  • [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
  • [26] Tephnadze G., A note on the norm convergence of Vilenkin-Fejér means, Georgian Math. J. (in press)
  • [27] Weisz F., Martingale Hardy Spaces and their Applications in Fourier Analysis, Lecture Notes in Math., 1568, Springer, Berlin, 1994
  • [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
  • [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] Weisz F., Convergence of double Walsh-Fourier series and Hardy spaces, Approx. Theory Appl. (N.S.), 2001, 17(2), 32–44
  • [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
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-014-0406-1
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.