An integral criterion for being an $H^1(ℝ^2)$ Fourier multiplier is proved. It is applied in particular to suitable regular functions which depend on the product of variables.
Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland
Bibliografia
[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.
[EG] R. E. Edwards and G. I. Gaudry, Littlewood-Paley and Multiplier Theory, Springer, 1977.
[FS] C. Fefferman and E. Stein, $H^p$ spaces of several variables, Acta Math. 129 (1972), 137-193.
[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.
[GR] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, 1985.
[Hö] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer, 1983.
[MZ] J. Marcinkiewicz and A. Zygmund, Quelques inégalités pour les opérations linéaires, Fund. Math. 32 (1939), 115-121.
[S] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970.
[T] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Academic Press, 1986.
[W1] M. Wojciechowski, A Marcinkiewicz type multiplier theorem for $H^1$ spaces on product domains, this issue, 273-287.
[W2] M. Wojciechowski, A necessary condition for weak type (1,1) of multiplier transforms, Canad. J. Math., to appear.