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Weighted weak $ (1,1)$ and weighted $ L\sp p$ estimates for oscillating kernels


Authors: Sagun Chanillo, Douglas S. Kurtz and Gary Sampson
Journal: Trans. Amer. Math. Soc. 295 (1986), 127-145
MSC: Primary 42A50; Secondary 42B20
DOI: https://doi.org/10.1090/S0002-9947-1986-0831193-7
MathSciNet review: 831193
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Abstract: Weak type $ (1,1)$ and strong type $ (p,p)$ inequalities are proved for operators defined by oscillating kernels. The techniques are sufficiently general to derive versions of these inequalities using weighted norms.


References [Enhancements On Off] (What's this?)

  • [1] S. Chanillo, Weighted norm inequalities for strongly singular convolution operators, Trans. Amer. Math. Soc. 281 (1984), 77-107. MR 719660 (84m:42032)
  • [2] S. Chanillo, D. S. Kurtz and G. Sampson, Weighted $ {L^p}$ estimates for oscillating kernels, Ark. Mat. 21 (1983), 233-257. MR 727347 (85k:42034)
  • [3] R. R. Coifman and R. Rochberg, Another characterization of $ BMO$, Proc. Amer. Math. Soc. 79 (1980), 249-254. MR 565349 (81b:42067)
  • [4] E. T. Copson, Asymptotic expansions, Cambridge Univ. Press, Cambridge, 1965. MR 0168979 (29:6234)
  • [5] C. Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9-36. MR 0257819 (41:2468)
  • [6] D. Geller and E. M. Stein, Estimates for singular convolution operators on the Heisenberg group, Math. Ann. 267 (1984), 1-15. MR 737332 (85h:43009)
  • [7] W. B. Jurkat and G. Sampson, 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. MR 611228 (84i:42033)
  • [8] A. Miyachi, On the weakly strongly singular integrals, Japan J. Math. (N.S.) 4 (1978), 221-262. MR 528872 (83b:42019)
  • [9] D. H. Phong and E. M. Stein, Singular integrals related to the Radon transform and boundary value problems, Proc. Nat. Acad. Sci. U.S.A. 80 (1983), 7697-7701. MR 728667 (86j:42024)
  • [10] F. Ricci and E. M. Stein (unpublished).
  • [11] G. Sampson, More on weak estimates for oscillating kernels. II, Indiana Univ. Math. J. 29 (1980), 349-360. MR 570686 (81h:44004b)
  • [12] S. Sjostrand, On the Riesz means of the solution of the Schrödinger equation, Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mat. Ser. III 24 (1970), 331-348. MR 0270219 (42:5110)
  • [13] E. M. Stein and G. Weiss, Interpolation of operators with change of measures, Trans. Amer. Math. Soc. 87 (1958), 159-172. MR 0092943 (19:1184d)
  • [14] J. O. Stromberg and A. Torchinsky, Weighted $ H_w^p$ spaces, $ 0 < p < \infty $, preprint.
  • [15] -, Weights, sharp maximal functions and Hardy spaces, Bull. Amer. Math. Soc. (N.S.) 3 (1980), 1053-1056. MR 585189 (81i:42021)
  • [16] -, Lectures on weighted Hardy spaces, preprint.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1986-0831193-7
Article copyright: © Copyright 1986 American Mathematical Society

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