Oscillatory singular integrals on weighted Hardy spaces

Yue Hu

Studia Mathematica (1992)

  • Volume: 102, Issue: 2, page 145-156
  • ISSN: 0039-3223

Abstract

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Let T f ( x ) = p . v . ʃ ℝ ¹ e i P ( x - y ) f ( y ) / ( x - y ) d y , where P is a real polynomial on ℝ. It is proved that T is bounded on the weighted H¹(wdx) space with w ∈ A₁.

How to cite

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Hu, Yue. "Oscillatory singular integrals on weighted Hardy spaces." Studia Mathematica 102.2 (1992): 145-156. <http://eudml.org/doc/215919>.

@article{Hu1992,
abstract = {Let $Tf(x) = p.v. ʃ_\{ℝ¹\} e^\{iP(x-y)\} f(y)/(x-y) dy$, where P is a real polynomial on ℝ. It is proved that T is bounded on the weighted H¹(wdx) space with w ∈ A₁.},
author = {Hu, Yue},
journal = {Studia Mathematica},
keywords = {oscillatory singular integrals; H¹ space; A₁ condition; weighted Hardy spaces; condition},
language = {eng},
number = {2},
pages = {145-156},
title = {Oscillatory singular integrals on weighted Hardy spaces},
url = {http://eudml.org/doc/215919},
volume = {102},
year = {1992},
}

TY - JOUR
AU - Hu, Yue
TI - Oscillatory singular integrals on weighted Hardy spaces
JO - Studia Mathematica
PY - 1992
VL - 102
IS - 2
SP - 145
EP - 156
AB - Let $Tf(x) = p.v. ʃ_{ℝ¹} e^{iP(x-y)} f(y)/(x-y) dy$, where P is a real polynomial on ℝ. It is proved that T is bounded on the weighted H¹(wdx) space with w ∈ A₁.
LA - eng
KW - oscillatory singular integrals; H¹ space; A₁ condition; weighted Hardy spaces; condition
UR - http://eudml.org/doc/215919
ER -

References

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  1. [1] S. Chanillo and M. Christ, Weak (1,1) bounds for oscillatory singular integrals, Duke Math. J. 55 (1987), 141-157. Zbl0667.42007
  2. [2] R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241-250. Zbl0291.44007
  3. [3] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Math. Stud. 116 [Notas Mat. 104], North-Holland, Amsterdam 1985. 
  4. [4] Y. Hu, A weighted norm inequality for oscillatory singular integrals, in: Lecture Notes in Math., to appear. 
  5. [5] Y. Hu, Weighted L p estimates for oscillatory integrals, preprint. 
  6. [6] D. H. Phong and E. M. Stein, Hilbert integrals, singular integrals, and Radon transforms I, Acta Math. 157 (1986), 99-157. Zbl0622.42011
  7. [7] F. Ricci and E. M. Stein, Harmonic analysis on nilpotent groups and singular integrals. I. Oscillatory integrals, J. Funct. Anal. 73 (1987), 179-194. Zbl0622.42010
  8. [8] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970. Zbl0207.13501
  9. [9] E. M. Stein and S. Wainger, Problems in harmonic analysis related to curvature, Bull. Amer. Math. Soc. 84 (1978), 1239-1295. Zbl0393.42010
  10. [10] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, N.J., 1970. Zbl0232.42007
  11. [11] R. Strichartz, Singular integrals supported on submanifolds, Studia Math. 74 (1982), 137-151. Zbl0501.43007
  12. [12] J.-O. Strömberg and A. Torchinsky, Weighted Hardy Spaces, Lecture Notes in Math. 1381, Springer, 1989. 
  13. [13] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Academic Press, Orlando, Fla., 1986. Zbl0621.42001
  14. [14] A. Zygmund, Trigonometric Series, 2nd ed., Cambridge Univ. Press, London 1959. Zbl0085.05601

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