A class of Fourier multipliers on H¹(ℝ²)

• Autorzy: Michał Wojciechowski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42B15: Multipliers
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)
• 42B30: H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2000
• Tom: 140
• Numer: 3
• Strony: 289-298

Daty

wydano

2000

otrzymano

1999-12-10

poprawiono

2000-03-31

Twórcy

autor

Michał Wojciechowski

• 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.