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Weighted inequalities for convolutions


Author: Kenneth F. Andersen
Journal: Proc. Amer. Math. Soc. 123 (1995), 1129-1136
MSC: Primary 44A10; Secondary 26D15, 44A35
DOI: https://doi.org/10.1090/S0002-9939-1995-1277088-X
MathSciNet review: 1277088
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Abstract: For certain convolution operators T on $ {R^ + }$ or $ {R^n}$, sufficient conditions are given which ensure that T is bounded between weighted Lebesgue spaces. The class of operators considered includes many of classical interest; in particular, new inequalities are obtained for the Laplace transform, the Poisson integral on $ {R^n} \times {R^ + }$, and Goldberg's transform.


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

  • [1] K. F. Andersen and B. Muckenhoupt, Weighted weak type Hardy inequalities with applications to Hilbert transforms and maximal functions, Studia Math. 72 (1982), 9-26. MR 665888 (83k:42018)
  • [2] S. Bloom, Hardy integral estimates for the Laplace transform, Proc. Amer. Math. Soc. 116 (1992), 417-426. MR 1094497 (92m:44002)
  • [3] J. S. Bradley, Hardy inequalities with mixed norms, Canad. Math. Bull. 21 (1978), 405-408. MR 523580 (80a:26005)
  • [4] G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Second Ed., Cambridge Univ. Press, Cambridge, 1967.
  • [5] R. R. Goldberg, An integral transform related to the Hilbert transform, J. London Math. Soc. 35 (1960), 200-204. MR 0110929 (22:1797)
  • [6] R. A. Hunt, B. Muckenhoupt, and R. Wheeden, Weighted norm inequalities for the conjugate function and Hilbert transform, Trans. Amer. Math. Soc. 176 (1973), 227-251. MR 0312139 (47:701)
  • [7] V. G. Maz'ja, Sobolev spaces, Springer-Verlag, Heidelberg, 1985. MR 817985 (87g:46056)
  • [8] B. Muckenhoupt, Hardy's inequality with weights, Studia Math. 44 (1972), 31-38. MR 0311856 (47:418)
  • [9] -, Two weight function norm inequalities for the Poisson integral, Trans. Amer. Math. Soc. 210 (1975), 225-231. MR 0374790 (51:10986)
  • [10] R. Wheeden and A. Zygmund, Measure and integral, Marcel Dekker, New York, 1980. MR 0492146 (58:11295)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1277088-X
Keywords: Weighted inequalities, convolution, integral operator
Article copyright: © Copyright 1995 American Mathematical Society

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