Weighted weak type (1,1) estimates for oscillatory singular integrals

Shuichi Sato

Studia Mathematica (2000)

  • Volume: 141, Issue: 1, page 1-24
  • ISSN: 0039-3223

Abstract

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We consider the A 1 -weights and prove the weighted weak type (1,1) inequalities for certain oscillatory singular integrals.

How to cite

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Sato, Shuichi. "Weighted weak type (1,1) estimates for oscillatory singular integrals." Studia Mathematica 141.1 (2000): 1-24. <http://eudml.org/doc/216770>.

@article{Sato2000,
abstract = {We consider the $A_1$-weights and prove the weighted weak type (1,1) inequalities for certain oscillatory singular integrals.},
author = {Sato, Shuichi},
journal = {Studia Mathematica},
keywords = {rough operators; oscillatory singular integrals; weighted weak space; Calderón-Zygmund convolution kernel; oscillatory singular integral operator},
language = {eng},
number = {1},
pages = {1-24},
title = {Weighted weak type (1,1) estimates for oscillatory singular integrals},
url = {http://eudml.org/doc/216770},
volume = {141},
year = {2000},
}

TY - JOUR
AU - Sato, Shuichi
TI - Weighted weak type (1,1) estimates for oscillatory singular integrals
JO - Studia Mathematica
PY - 2000
VL - 141
IS - 1
SP - 1
EP - 24
AB - We consider the $A_1$-weights and prove the weighted weak type (1,1) inequalities for certain oscillatory singular integrals.
LA - eng
KW - rough operators; oscillatory singular integrals; weighted weak space; Calderón-Zygmund convolution kernel; oscillatory singular integral operator
UR - http://eudml.org/doc/216770
ER -

References

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  1. [1] S. Chanillo, Weighted norm inequalities for strongly singular convolution operators, Trans. Amer. Math. Soc. 281 (1984), 77-107. Zbl0531.42005
  2. [2] S. Chanillo and M. Christ, Weak (1,1) bounds for oscillatory singular integrals, Duke Math. J. 55 (1987), 141-155. Zbl0667.42007
  3. [3] S. Chanillo, D. S. Kurtz and G. Sampson, Weighted weak (1,1) and weighted L p estimates for oscillating kernels, Trans. Amer. Math. Soc. 295 (1986), 127-145. Zbl0594.42007
  4. [4] M. Christ, Hilbert transforms along curves, I: Nilpotent groups, Ann. of Math. 122 (1985), 575-596. Zbl0593.43011
  5. [5] M. Christ, Weak type (1,1) bounds for rough operators, ibid. 128 (1988), 19-42. Zbl0666.47027
  6. [6] M. Christ, Weak type endpoint bounds for Bochner-Riesz multipliers, Rev. Mat. Iberoamericana 3 (1987), 25-31. Zbl0726.42009
  7. [7] M. Christ and J. L. Rubio de Francia, Weak type (1,1) bounds for rough operators, II, Invent. Math. 93 (1988), 225-237. Zbl0695.47052
  8. [8] J.-L. Journé, Calderón-Zygmund Operators, Pseudo-Differential Operators and the Cauchy Integral of Calderón, Lecture Notes in Math. 994, Springer, 1983. Zbl0508.42021
  9. [9] F. Ricci and E. M. Stein, Harmonic analysis on nilpotent groups and singular integrals, I, J. Funct. Anal. 73 (1987), 179-194. Zbl0622.42010
  10. [10] S. Sato, Some weighted weak type estimates for rough operators, Math. Nachr. 187 (1997), 211-240. Zbl0926.42012
  11. [11] A. Vargas, Weighted weak type (1,1) bounds for rough operators, J. London Math. Soc. (2) 54 (1996), 297-310 Zbl0884.42011

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