A class of Fourier multipliers on H¹(ℝ²)
Wojciechowski, Michał
Studia Mathematica, Tome 141 (2000), p. 289-298 / Harvested from The Polish Digital Mathematics Library

An integral criterion for being an H1(2) Fourier multiplier is proved. It is applied in particular to suitable regular functions which depend on the product of variables.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:216768
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     author = {Micha\l\ Wojciechowski},
     title = {A class of Fourier multipliers on H$^1$($\mathbb{R}$$^2$)},
     journal = {Studia Mathematica},
     volume = {141},
     year = {2000},
     pages = {289-298},
     zbl = {0982.42005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv140i3p289bwm}
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Wojciechowski, Michał. A class of Fourier multipliers on H¹(ℝ²). Studia Mathematica, Tome 141 (2000) pp. 289-298. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv140i3p289bwm/

[00000] [BBPW] E. Berkson, J. Bourgain, A. Pełczyński and M. Wojciechowski, Canonical Sobolev projections which are of weak type (1,1), Mem. Amer. Math. Soc., to appear. | Zbl 0990.42005

[00001] [EG] R. E. Edwards and G. I. Gaudry, Littlewood-Paley and Multiplier Theory, Springer, 1977.

[00002] [FS] C. Fefferman and E. Stein, Hp spaces of several variables, Acta Math. 129 (1972), 137-193. | Zbl 0257.46078

[00003] [F] R. Fefferman, Some topics from harmonic analysis and partial differential equations, in: Essays on Fourier Analysis in Honor of Elias M. Stein, Princeton Univ. Press, 1995, 175-210. | Zbl 0834.42010

[00004] [GR] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, 1985.

[00005] [Hö] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer, 1983.

[00006] [MZ] J. Marcinkiewicz and A. Zygmund, Quelques inégalités pour les opérations linéaires, Fund. Math. 32 (1939), 115-121. | Zbl 65.0506.02

[00007] [S] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970. | Zbl 0207.13501

[00008] [T] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Academic Press, 1986. | Zbl 0621.42001

[00009] [W1] M. Wojciechowski, A Marcinkiewicz type multiplier theorem for H1 spaces on product domains, this issue, 273-287. | Zbl 0982.42004

[00010] [W2] M. Wojciechowski, A necessary condition for weak type (1,1) of multiplier transforms, Canad. J. Math., to appear.