An oscillatory singular integral operator with polynomial phase

Josfina Alvarez; Jorge Hounie

Studia Mathematica (1999)

  • Volume: 133, Issue: 1, page 1-18
  • ISSN: 0039-3223

Abstract

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We prove the continuity of an oscillatory singular integral operator T with polynomial phase P(x,y) on an atomic space H P 1 related to the phase P. Moreover, we show that the cancellation condition to be imposed on T holds under more general conditions. To that purpose, we obtain a van der Corput type lemma with integrability at infinity.

How to cite

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Alvarez, Josfina, and Hounie, Jorge. "An oscillatory singular integral operator with polynomial phase." Studia Mathematica 133.1 (1999): 1-18. <http://eudml.org/doc/216602>.

@article{Alvarez1999,
abstract = {We prove the continuity of an oscillatory singular integral operator T with polynomial phase P(x,y) on an atomic space $H_P^1$ related to the phase P. Moreover, we show that the cancellation condition to be imposed on T holds under more general conditions. To that purpose, we obtain a van der Corput type lemma with integrability at infinity.},
author = {Alvarez, Josfina, Hounie, Jorge},
journal = {Studia Mathematica},
keywords = {oscillatory singular integral; Calderón-Zygmund kernel; atom; molecule; Hardy space; BMO; van der Corput lemma},
language = {eng},
number = {1},
pages = {1-18},
title = {An oscillatory singular integral operator with polynomial phase},
url = {http://eudml.org/doc/216602},
volume = {133},
year = {1999},
}

TY - JOUR
AU - Alvarez, Josfina
AU - Hounie, Jorge
TI - An oscillatory singular integral operator with polynomial phase
JO - Studia Mathematica
PY - 1999
VL - 133
IS - 1
SP - 1
EP - 18
AB - We prove the continuity of an oscillatory singular integral operator T with polynomial phase P(x,y) on an atomic space $H_P^1$ related to the phase P. Moreover, we show that the cancellation condition to be imposed on T holds under more general conditions. To that purpose, we obtain a van der Corput type lemma with integrability at infinity.
LA - eng
KW - oscillatory singular integral; Calderón-Zygmund kernel; atom; molecule; Hardy space; BMO; van der Corput lemma
UR - http://eudml.org/doc/216602
ER -

References

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  8. [8] Y. Hu, Oscillatory singular integrals on weighted Hardy spaces, Studia Math. 102 (1992), 145-156. Zbl0808.42009
  9. [9] Y. Hu and Y. Pan, Boundedness of oscillatory singular integrals on Hardy spaces, Ark. Mat. 30 (1992), 311-320. Zbl0779.42007
  10. [10] Y. Pan, Hardy spaces and oscillatory singular integrals, Rev. Mat. Iberoamericana 7 (1991), 55-64. Zbl0728.42013
  11. [11] D. H. Phong and E. M. Stein, Hilbert integrals, singular integrals, and Radon transforms, I, Acta Math. 157 (1986), 99-157. Zbl0622.42011
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  13. [13] E. M. Stein, Oscillatory integrals in Fourier analysis, in: Beijing Lectures in Harmonic Analysis, Princeton Univ. Press, 1986, 307-355. 

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