ArticleOriginal scientific text

Title

On conjugate Poisson integrals and Riesz transforms for the Hermite expansions

Authors 1

Affiliations

  1. Tata Institute of Fundamental Research, Post Box NO. 1234, I.I.SC Campus, Bangalore 560 012, India

Bibliography

  1. R. Askey and S. Wainger, Mean convergence of expansions in Laguerre and Hermite series, Amer. J. Math. 87 (1965), 695-708.
  2. G. B. Folland, Harmonic Analysis in Phase Space, Ann. of Math. Stud. 122, Princeton Univ. Press, Princeton, N.J., 1989.
  3. D. Goldberg, A local version of real Hardy spaces, Duke Math. J. 46 (1979), 27-42.
  4. P. A. Meyer, Transformations de Riesz pour les lois Gaussiens, in: Séminaire de Probabilités 18, Lecture Notes in Math. 1059, Springer, 1984, 179-193.
  5. B. Muckenhoupt, Hermite conjugate expansions, Trans. Amer. Math. Soc. 139 (1969), 243-260.
  6. B. Muckenhoupt and E. Stein, Classical expansions and their relations to conjugate harmonic functions, ibid. 118 (1965), 17-92.
  7. G. Pisier, Riesz transforms: a simpler analytic proof of P. A. Meyer's inequality, preprint.
  8. E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1971.
  9. S. Thangavelu, Summability of Hermite expansions I, Trans. Amer. Math. Soc. 314 (1989), 119-142.
  10. S. Thangavelu, Summability of Hermite expansions II, ibid., 143-170.
  11. S. Thangavelu, Riesz transforms and the wave equation for the Hermite operator, Comm. Partial Differential Equations 15 (1990), 1199-1215.
  12. S. Thangavelu, On almost everywhere and mean convergence of Hermite and Laguerre expansions, Colloq. Math. 60 (1990), 21-34.
  13. W. Urbina, On singular integrals with respect to Gaussian measures, Ann. Scuola Norm. Sup. Pisa 17 (1990), 531-567.
Pages:
103-113
Main language of publication
English
Received
1991-04-08
Accepted
1992-01-15
Published
1993
Exact and natural sciences