PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1995 | 114 | 2 | 105-116
Tytuł artykułu

Boundedness of certain oscillatory singular integrals

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove the $L^p$ and $H^1$ boundedness of oscillatory singular integral operators defined by Tf = p.v.Ω∗f, where $Ω(x) = e^{iΦ(x)}K(x)$, K(x) is a Calderón-Zygmund kernel, and Φ satisfies certain growth conditions.
Słowa kluczowe
Czasopismo
Rocznik
Tom
114
Numer
2
Strony
105-116
Opis fizyczny
Daty
wydano
1995
otrzymano
1993-08-31
Twórcy
autor
  • epartment of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WIsconsin 53201, U.S.A.
autor
  • Department of Mathematical and Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A.
Bibliografia
  • [1] S. Chanillo, Weighted norm inequalities for strongly singular convolution operators, Trans. Amer. Math. Soc. 281 (1984), 77-107.
  • [2] S. Chanillo and M. Christ, Weak (1,1) bounds for oscillatory singular integrals, Duke Math. J. 55 (1987), 141-155.
  • [3] S. Chanillo, D. Kurtz and G. Sampson, Weighted weak (1,1) and weighted $L^p$ estimates for oscillating kernels, Trans. Amer. Math. Soc. 295 (1986), 127-145.
  • [4] R. Coifman, A real variable characterization of $H^p$, Studia Math. 51 (1974), 269-274.
  • [5] R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645.
  • [6] D. Fan, An oscillating integral in the Besov space $B^1, 0_0 (ℝ^n)$, submitted for publication.
  • [7] C. Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9-36.
  • [8] C. Fefferman and E. M. Stein, $H^p$ spaces of several variables, ibid. 129 (1972), 137-193.
  • [9] Y. Hu and Y. Pan, Boundedness of oscillatory singular integrals on Hardy spaces, Ark. Mat. 30 (1992), 311-320.
  • [10] W. B. Jurkat and G. Sampson, The complete solution to the $(L^p, L^q)$ mapping problem for a class of oscillating kernels, Indiana Univ. Math. J. 30 (1981), 403-413.
  • [11] Y. Pan, Uniform estimates for oscillatory integral operators, J. Funct. Anal. 100 (1991), 207-220.
  • [12] Y. Pan, Hardy spaces and oscillatory singular integrals, Rev. Mat. Iberoamericana 7 (1991), 55-64.
  • [13] Y. Pan, Boundedness of oscillatory singular integrals on Hardy spaces: II, Indiana Univ. Math. J. 41 (1992), 279-293.
  • [14] D. H. Phong and E. M. Stein, Hilbert integrals, singular integrals and Radon transforms I, Acta Math. 157 (1986), 99-157.
  • [15] F. Ricci and E. M. Stein, Harmonic analysis on nilpotent groups and singular integrals I, J. Funct. Anal. 73 (1987), 179-194.
  • [16] G. Sampson, Oscillating kernels that map $H^1$ into $L^1$, Ark. Mat. 18 (1981), 125-144.
  • [17] P. Sjölin, Convolution with oscillating kernels on $H^p$ spaces, J. London Math. Soc. 23 (1981), 442-454.
  • [18] P. Sjölin, Convolution with oscillating kernels, Indiana Univ. Math. J. 30 (1981), 47-55.
  • [19] M. Spivak, Calculus on Manifolds, Addison-Wesley, New York, N.Y., 1992.
  • [20] E. M. Stein, Oscillatory integrals in Fourier analysis, in: Beijing Lectures in Harmonic Analysis, Princeton Univ. Press, Princeton, N.J., 1986, pp. 307-355.
  • [21] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, Princeton, N.J., 1993.
  • [22] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, N.J., 1971.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv114i2p105bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.