On conjugate Poisson integrals and Riesz transforms for the Hermite expansions

S. Thangavelu

Colloquium Mathematicae (1993)

  • Volume: 64, Issue: 1, page 103-113
  • ISSN: 0010-1354

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Thangavelu, S.. "On conjugate Poisson integrals and Riesz transforms for the Hermite expansions." Colloquium Mathematicae 64.1 (1993): 103-113. <http://eudml.org/doc/210159>.

@article{Thangavelu1993,
author = {Thangavelu, S.},
journal = {Colloquium Mathematicae},
keywords = {conjugate Poisson integrals; Hermite function expansions; Riesz transforms; Hermite operator},
language = {eng},
number = {1},
pages = {103-113},
title = {On conjugate Poisson integrals and Riesz transforms for the Hermite expansions},
url = {http://eudml.org/doc/210159},
volume = {64},
year = {1993},
}

TY - JOUR
AU - Thangavelu, S.
TI - On conjugate Poisson integrals and Riesz transforms for the Hermite expansions
JO - Colloquium Mathematicae
PY - 1993
VL - 64
IS - 1
SP - 103
EP - 113
LA - eng
KW - conjugate Poisson integrals; Hermite function expansions; Riesz transforms; Hermite operator
UR - http://eudml.org/doc/210159
ER -

References

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  1. [1] R. Askey and S. Wainger, Mean convergence of expansions in Laguerre and Hermite series, Amer. J. Math. 87 (1965), 695-708. Zbl0125.31301
  2. [2] G. B. Folland, Harmonic Analysis in Phase Space, Ann. of Math. Stud. 122, Princeton Univ. Press, Princeton, N.J., 1989. Zbl0682.43001
  3. [3] D. Goldberg, A local version of real Hardy spaces, Duke Math. J. 46 (1979), 27-42. Zbl0409.46060
  4. [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. [5] B. Muckenhoupt, Hermite conjugate expansions, Trans. Amer. Math. Soc. 139 (1969), 243-260. Zbl0175.12701
  6. [6] B. Muckenhoupt and E. Stein, Classical expansions and their relations to conjugate harmonic functions, ibid. 118 (1965), 17-92. Zbl0139.29002
  7. [7] G. Pisier, Riesz transforms: a simpler analytic proof of P. A. Meyer's inequality, preprint. Zbl0645.60061
  8. [8] E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1971. 
  9. [9] S. Thangavelu, Summability of Hermite expansions I, Trans. Amer. Math. Soc. 314 (1989), 119-142. Zbl0685.42015
  10. [10] S. Thangavelu, Summability of Hermite expansions II, ibid., 143-170. Zbl0685.42016
  11. [11] S. Thangavelu, Riesz transforms and the wave equation for the Hermite operator, Comm. Partial Differential Equations 15 (1990), 1199-1215. Zbl0709.35068
  12. [12] S. Thangavelu, On almost everywhere and mean convergence of Hermite and Laguerre expansions, Colloq. Math. 60 (1990), 21-34. Zbl0747.42014
  13. [13] W. Urbina, On singular integrals with respect to Gaussian measures, Ann. Scuola Norm. Sup. Pisa 17 (1990), 531-567. Zbl0737.42018

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