L 2 and L p estimates for oscillatory integrals and their extended domains

Yibiao Pan; Gary Sampson; Paweł Szeptycki

Studia Mathematica (1997)

  • Volume: 122, Issue: 3, page 201-224
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Pan, Yibiao, Sampson, Gary, and Szeptycki, Paweł. "$L^{2}$ and $L^{p}$ estimates for oscillatory integrals and their extended domains." Studia Mathematica 122.3 (1997): 201-224. <http://eudml.org/doc/216372>.

@article{Pan1997,
abstract = {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.},
author = {Pan, Yibiao, Sampson, Gary, Szeptycki, Paweł},
journal = {Studia Mathematica},
keywords = {$L^p$ boundedness; oscillatory integrals; extended domains; Calderón-Zygmund kernels; boundedness; oscillatory singular integral operators},
language = {eng},
number = {3},
pages = {201-224},
title = {$L^\{2\}$ and $L^\{p\}$ estimates for oscillatory integrals and their extended domains},
url = {http://eudml.org/doc/216372},
volume = {122},
year = {1997},
}

TY - JOUR
AU - Pan, Yibiao
AU - Sampson, Gary
AU - Szeptycki, Paweł
TI - $L^{2}$ and $L^{p}$ estimates for oscillatory integrals and their extended domains
JO - Studia Mathematica
PY - 1997
VL - 122
IS - 3
SP - 201
EP - 224
AB - 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.
LA - eng
KW - $L^p$ boundedness; oscillatory integrals; extended domains; Calderón-Zygmund kernels; boundedness; oscillatory singular integral operators
UR - http://eudml.org/doc/216372
ER -

References

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  6. [LS] Labuda, I. and Szeptycki, P., Extended domains of some integral operators with rapidly oscillating kernels, Nederl. Akad. Wetensch. Proc. 89 (1986), 87-98. Zbl0622.47032
  7. [LS2] Labuda, Extensions of integral operators, Math. Ann. 281 (1988), 341-353. Zbl0617.45013
  8. [M] Muckenhoupt, B., Weighted norm inequalities for the Hardy-Littlewood maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226. Zbl0236.26016
  9. [Pan] Pan, Y., Hardy spaces and oscillatory singular integrals, Rev. Mat. Iberoamericana 7 (1991), 55-64. Zbl0728.42013
  10. [PS] Phong, D.H. and Stein, E.M., Hilbert integrals, singular integrals, and Radon transforms I, Acta Math. 157 (1986), 99-157. Zbl0622.42011
  11. [Sj] Sjölin, P., Regularity of solutions to the Schrödinger equation, Duke Math. J. 55 (1987), 699-715. Zbl0631.42010
  12. [St] Stein, E.M., Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals, Princeton Univ. Press, Princeton, N.J., 1993. 
  13. [Sz] Szeptycki,P., Extended domains of some integral operators, Rocky Mountain J. Math. 22 (1992), 393-404. Zbl0761.47026
  14. [Wal] Walther, B.G., Maximal estimates for oscillatory integrals with concave phase, preprint, 1994. 
  15. [Zyg] Zygmund, A., Trigonometric Series, Cambridge Univ. Press, Cambridge, 1959. 

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