PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1997 | 122 | 3 | 201-224
Tytuł artykułu

$L^{2}$ and $L^{p}$ estimates for oscillatory integrals and their extended domains

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove the $L^p$ boundedness of certain nonconvolutional oscillatory integral operators and give explicit description of their extended domains. The class of phase functions considered here includes the function $|x|^{α}|y|^{β}$. Sharp boundedness results are obtained in terms of α, β, and rate of decay of the kernel at infinity.
Twórcy
autor
  • Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A., yibiao+@pitt.edu
autor
Bibliografia
  • [AS] Aronszajn, N. and Szeptycki, P., On general integral transformations, Math. Ann. 163 (1966), 127-154.
  • [FS] J. J. F. Fournier and Stewart, J., Amalgams of $L^p$ and $l^q$, Bull. Amer. Math. Soc. 13 (1985), 1-21.
  • [G] Gagliardo, E., On integral transformations with positive kernels, Proc. Amer. Math. Soc. 16 (1965), 429-434.
  • [Ho] Hörmander, L., The Analysis of Linear Partial Differential Operators I, Springer, Berlin, 1983.
  • [JS] Jurkat, W.B. and Sampson, G., 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.
  • [LS] Labuda, I. and Szeptycki, P., Extended domains of some integral operators with rapidly oscillating kernels, Nederl. Akad. Wetensch. Proc. 89 (1986), 87-98.
  • [LS2] Labuda, Extensions of integral operators, Math. Ann. 281 (1988), 341-353.
  • [M] Muckenhoupt, B., Weighted norm inequalities for the Hardy-Littlewood maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226.
  • [Pan] Pan, Y., Hardy spaces and oscillatory singular integrals, Rev. Mat. Iberoamericana 7 (1991), 55-64.
  • [PS] Phong, D.H. and Stein, E.M., Hilbert integrals, singular integrals, and Radon transforms I, Acta Math. 157 (1986), 99-157.
  • [Sj] Sjölin, P., Regularity of solutions to the Schrödinger equation, Duke Math. J. 55 (1987), 699-715.
  • [St] Stein, E.M., Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals, Princeton Univ. Press, Princeton, N.J., 1993.
  • [Sz] Szeptycki,P., Extended domains of some integral operators, Rocky Mountain J. Math. 22 (1992), 393-404.
  • [Wal] Walther, B.G., Maximal estimates for oscillatory integrals with concave phase, preprint, 1994.
  • [Zyg] Zygmund, A., Trigonometric Series, Cambridge Univ. Press, Cambridge, 1959.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv122i3p201bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.