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2000 | 140 | 3 | 273-287
Tytuł artykułu

A Marcinkiewicz type multiplier theorem for H¹ spaces on product domains

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is proved that if $m : ℝ^d → ℂ$ satisfies a suitable integral condition of Marcinkiewicz type then m is a Fourier multiplier on the $H^1$ space on the product domain $ℝ^{d_1}×...×ℝ^{d_k}$. This implies an estimate of the norm $N(m,L^p(ℝ^d)$ of the multiplier transformation of m on $L^p(ℝ^d)$ as p→1. Precisely we get $N(m,L^p(ℝ^d))≲(p-1)^{-k}$. This bound is the best possible in general.
Słowa kluczowe
Czasopismo
Rocznik
Tom
140
Numer
3
Strony
273-287
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-12-10
poprawiono
2000-03-31
Twórcy
  • Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland, miwoj@impan.gov.pl
Bibliografia
  • E. Berkson, J. Bourgain, A. Pełczyński and M. Wojciechowski, Canonical Sobolev projections which are of weak type (1,1), submitted to Mem. Amer. Math. Soc.
  • [B] J. Bourgain, On the behavior of the constant in the Littlewood-Paley inequality, in: Geometric Aspects of Functional Analysis, Lecture Notes in Math. 1376, Springer, 1989, 202-208.
  • [C] L. Carleson, Two remarks on $H^1$ and BMO, Adv. Math. 22 (1976), 269-277.
  • S. Y. A. Chang and R. Fefferman, The Calderón-Zygmund decomposition on product domains, Amer. J. Math. 104 (1982), 455-468.
  • S. Y. A. Chang and R. Fefferman, Some recent developments in Fourier analysis and $H^p$ theory on product domains, Bull. Amer. Math. Soc. 12 (1985), 1-43.
  • [D] N. Dunford, Spectral operators, Pacific J. Math. 4 (1954), 321-354.
  • [EG] R. E. Edwards and G. I. Gaudry, Littlewood-Paley and Multiplier Theory, Springer, 1977.
  • [FS] C. Fefferman and E. M. Stein, Hardy spaces of several variables, Acta Math. 129 (1972), 137-193.
  • [F1] R. Fefferman, Harmonic analysis on product spaces, Ann. of Math. 126 (1987), 109-130.
  • [F2] 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.
  • [Hö] L. Hö rmander, The Analysis of Linear Partial Differential Operators I, Springer, 1983.
  • [Lu] S. Z. Lu, Four Lectures on Real $H^p$ Spaces, World Sci., 1995.
  • [M] V. G. Maz'ya, Sobolev Spaces, Leningrad Univ. Press, 1985.
  • [Mu] P. F. X. Müller, Holomorphic martingales and interpolation between Hardy spaces, J. Anal. Math. 61 (1993), 327-337.
  • [MC] C. A. McCarthy, $c_p$, Israel J. Math. 5 (1967), 249-271.
  • [P] A. Pełczyński, Boundedness of the canonical projection for Sobolev spaces generated by finite families of linear differential operators, in: Analysis at Urbana 1 (Proceedings of Special Year in Modern Analysis at the Univ. of Illinois, 1986-87), London Math. Soc. Lecture Note Ser. 137, Cambridge Univ. Press 1989, 395-415.
  • [S] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, 1970.
  • [TW] M. H. Taibleson and G. Weiss, The molecular characterization of certain Hardy spaces, Astérisque 77 (1980), 67-149.
  • [T] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Academic Press, 1986.
  • [X] Q. Xu, Some properties of the quotient space $L^1(T^d)/H^1(D^d)$, Illinois J. Math. 37 (1993), 437-454.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv140i3p273bwm
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