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Transactions of the American Mathematical Society

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Singular integrals and approximate identities on spaces of homogeneous type


Author: Hugo Aimar
Journal: Trans. Amer. Math. Soc. 292 (1985), 135-153
MSC: Primary 42B20; Secondary 42B25
DOI: https://doi.org/10.1090/S0002-9947-1985-0805957-9
MathSciNet review: 805957
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Abstract: In this paper we give conditions for the $ {L^2}$-boundedness of singular integrals and the weak type $ (1,1)$ of approximate identities on spaces of homogeneous type. Our main tools are Cotlar's lemma and an extension of a theorem of Zó.


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  • [CG] R. Coifman and M. de Guzmán, Singular integrals and multipliers on homogeneous spaces, Rev. Un. Mat. Argentina 25 (1970), 137-144. MR 0320644 (47:9180)
  • [CW] R. Coifman and G. Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, ètude de certaines intégrales singulières, Lecture Notes in Math., vol. 242, Springer-Verlag, Berlin, 1971. MR 0499948 (58:17690)
  • [G] M. de Guzman, Real variable methods in Fourier analysis, Notas de Matemática (75), North-Holland Math. Studies, No. 46, North-Holland, Amsterdam, 1981. MR 596037 (83j:42019)
  • [GGW] A. Gatto, C. Gutierrez and R. Wheeden, On weighted fractional integrals, Conference on Harmonic Analysis, In Honor of Antoni Zygmund, Wadsworth, Belmont, Calif., 1983, pp. 124-137. MR 730063 (85f:26010)
  • [MS1] R. Macías and C. Segovia, Lipschitz functions on spaces of homogeneous type, Adv. in Math. 33 (1979), 257-270. MR 546295 (81c:32017a)
  • [MS2] -, A decomposition into atoms of distributions on spaces of homogeneous type, Adv. in Math. 33 (1979), 271-309. MR 546296 (81c:32017b)
  • [R] N. Riviere, Singular integrals and multiplier operators, Ark. Mat. 9 (1973), 243-270. MR 0440268 (55:13146)
  • [Z] F. Zø, A note on the approximation of the identity, Studia Math. 55 (1976), 111-122. MR 0423013 (54:10997)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1985-0805957-9
Keywords: Singular integrals, maximal functions, spaces of homogeneous type
Article copyright: © Copyright 1985 American Mathematical Society

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