[1] Nie J, Li X, Lou G. The martingale Hardy type inequalities for dyadic derivative and integral. Acta Mathematica Sinica, English Series, 2005, 21(6): 1465–1474
[2] Butzer P L, Wagner H J. Walsh series and the concept of a derivative. Appl Anal, 1973, 3: 29–46
[3] Schipp F, Wade W R, Simon P, Pál J. Walsh Series: An Introduction to Dyadic Harmonic Analysis. Bristol, New York: Adam Hilger, 1990
[4] Schipp F. Übereinen Ableitung sbegriff von P. L. Butzer and H. J. Wagner. Mat Balkanica, 1974, 4: 541–546
[5] Pál J, Simon P. On a generalization oft he concept of the derivative. Acta Math Hungar, 1977, 29: 55–164
[6] Marcinkiewicz J, Zygmund A. On the summability of double Fourier series. Fund Math, 1939, 32: 122–132
[7] Weisz F. The two-parameter dyadic derivative and dyadic Hardy spaces. Anal Math, 2003, 26: 143–160
[8] Goginava U. The Hardy type inequality for the maximal operator of the one-dimensional dyadic derivative. Acta Math Sci, 2011, 31B(4): 1489–1493
[9] Butzer P L, Engels W. Dyadic calculus and sampling theorems for functions with multidimensional domain. Information and Control, 1982, 52: 33–351
[10] Gat G, Nagy K. The fundamental theorem of two-parameter pointwise derivative on Vilenkin groups. Analysis Mathematica, 1999, 25: 33–55
[11] Simon P, Weisz F. On the two parameter Vilenkin derivative. Math Pan, 2001, 12(1):105-128.
[12] Riyan C, Shixin G. Atomic decompositions for two-parameter vector-valued martingales and two-parameter vector-valued martingale spaces. Acta Math Hungar, 2001, 93(1/2): 7–25
[13] Liu Peide. Martingales and Geometry in Banach Spaces. Beijing: Scientific Press, 2007 |