(Hp,Lp)-type inequalities for the two-dimensional dyadic derivative
Weisz, Ferenc
Studia Mathematica, Tome 119 (1996), p. 271-288 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

It is shown that the restricted maximal operator of the two-dimensional dyadic derivative of the dyadic integral is bounded from the two-dimensional dyadic Hardy-Lorentz space Hp,q to Lp,q (2/3 < p < ∞, 0 < q ≤ ∞) and is of weak type (L1,L1). As a consequence we show that the dyadic integral of a ∞ function f∈L1 is dyadically differentiable and its derivative is f a.e.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:216337 
@article{bwmeta1.element.bwnjournal-article-smv120i3p271bwm,
     author = {Ferenc Weisz},
     title = {$(H\_p,L\_p)$-type inequalities for the two-dimensional dyadic derivative},
     journal = {Studia Mathematica},
     volume = {119},
     year = {1996},
     pages = {271-288},
     zbl = {0860.42022},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv120i3p271bwm}
}

Weisz, Ferenc. $(H_p,L_p)$-type inequalities for the two-dimensional dyadic derivative. Studia Mathematica, Tome 119 (1996) pp. 271-288. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv120i3p271bwm/

[00000] [1] C. Bennett and R. Sharpley, Interpolation of Operators, Pure Appl. Math. 129, Academic Press, New York, 1988. | Zbl 0647.46057

[00001] [2] J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, Berlin, 1976. | Zbl 0344.46071

[00002] [3] P. L. Butzer and W. Engels, Dyadic calculus and sampling theorems for functions with multidimensional domain, Inform. and Control 52 (1982), 333-351. | Zbl 0514.42028

[00003] [4] P. L. Butzer and H. J. Wagner, On dyadic analysis based on the pointwise dyadic derivative, Anal. Math. 1 (1975), 171-196. | Zbl 0324.42011

[00004] [5] P. L. Butzer and H. J. Wagner, Walsh series and the concept of a derivative, Appl. Anal. 3 (1973), 29-46. | Zbl 0256.42016

[00005] [6] A. M. Garsia, Martingale Inequalities. Seminar Notes on Recent Progress, Math. Lecture Notes Ser., Benjamin, New York, 1973.

[00006] [7] Gy. Gát, On the two-dimensional pointwise dyadic calculus, J. Approx. Theory, to appear. | Zbl 1127.42024

[00007] [8] J. Neveu, Discrete-Parameter Martingales, North-Holland, 1971.

[00008] [9] F. Schipp, Über einen Ableitungsbegriff von P. L. Butzer und H. J. Wagner, Math. Balkanica 4 (1974), 541-546.

[00009] [10] F. Schipp, Über gewissen Maximaloperatoren, Ann. Univ. Sci. Budapest. Sect. Math. 18 (1975), 189-195.

[00010] [11] F. Schipp and P. Simon, On some (H,L1)-type maximal inequalities with respect to the Walsh-Paley system, in: Functions, Series, Operators, Budapest 1980, Colloq. Math. Soc. János Bolyai 35, North-Holland, Amsterdam, 1981, 1039-1045.

[00011] [12] F. Schipp and W. R. Wade, A fundamental theorem of dyadic calculus for the unit square, Appl. Anal. 34 (1989), 203-218. | Zbl 0727.42020

[00012] [13] F. Schipp, W. R. Wade, P. Simon and J. Pál, Walsh Series: An Introduction to Dyadic Harmonic Analysis, Adam Hilger, Bristol, 1990. | Zbl 0727.42017

[00013] [14] F. Weisz, Cesàro summability of two-dimensional Walsh-Fourier series, Trans. Amer. Math. Soc. (1996), to appear. | Zbl 0866.42020

[00014] [15] F. Weisz, Martingale Hardy spaces and the dyadic derivative, Anal. Math., to appear. | Zbl 0914.42020

[00015] [16] F. Weisz, Martingale Hardy Spaces and Their Applications in Fourier-Analysis, Lecture Notes in Math. 1568, Springer, Berlin, 1994. | Zbl 0796.60049

[00016] [17] F. Weisz, Some maximal inequalities with respect to two-dimensional dyadic derivative and Cesàro summability, Appl. Anal., to appear. | Zbl 0861.42021

[00017] [18] A. Zygmund, Trigonometric Series, Cambridge Univ. Press, London, 1959. | Zbl 0085.05601