On conjugate Poisson integrals and Riesz transforms for the Hermite expansions
Thangavelu, S.
Colloquium Mathematicae, Tome 66 (1993), p. 103-113 / Harvested from The Polish Digital Mathematics Library
Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:210159
@article{bwmeta1.element.bwnjournal-article-cmv64i1p103bwm,
     author = {S. Thangavelu},
     title = {On conjugate Poisson integrals and Riesz transforms for the Hermite expansions},
     journal = {Colloquium Mathematicae},
     volume = {66},
     year = {1993},
     pages = {103-113},
     zbl = {0821.42016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv64i1p103bwm}
}
Thangavelu, S. On conjugate Poisson integrals and Riesz transforms for the Hermite expansions. Colloquium Mathematicae, Tome 66 (1993) pp. 103-113. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv64i1p103bwm/

[000] [1] R. Askey and S. Wainger, Mean convergence of expansions in Laguerre and Hermite series, Amer. J. Math. 87 (1965), 695-708. | Zbl 0125.31301

[001] [2] G. B. Folland, Harmonic Analysis in Phase Space, Ann. of Math. Stud. 122, Princeton Univ. Press, Princeton, N.J., 1989. | Zbl 0682.43001

[002] [3] D. Goldberg, A local version of real Hardy spaces, Duke Math. J. 46 (1979), 27-42. | Zbl 0409.46060

[003] [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.

[004] [5] B. Muckenhoupt, Hermite conjugate expansions, Trans. Amer. Math. Soc. 139 (1969), 243-260. | Zbl 0175.12701

[005] [6] B. Muckenhoupt and E. Stein, Classical expansions and their relations to conjugate harmonic functions, ibid. 118 (1965), 17-92. | Zbl 0139.29002

[006] [7] G. Pisier, Riesz transforms: a simpler analytic proof of P. A. Meyer's inequality, preprint. | Zbl 0645.60061

[007] [8] E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1971.

[008] [9] S. Thangavelu, Summability of Hermite expansions I, Trans. Amer. Math. Soc. 314 (1989), 119-142. | Zbl 0685.42015

[009] [10] S. Thangavelu, Summability of Hermite expansions II, ibid., 143-170. | Zbl 0685.42016

[010] [11] S. Thangavelu, Riesz transforms and the wave equation for the Hermite operator, Comm. Partial Differential Equations 15 (1990), 1199-1215. | Zbl 0709.35068

[011] [12] S. Thangavelu, On almost everywhere and mean convergence of Hermite and Laguerre expansions, Colloq. Math. 60 (1990), 21-34. | Zbl 0747.42014

[012] [13] W. Urbina, On singular integrals with respect to Gaussian measures, Ann. Scuola Norm. Sup. Pisa 17 (1990), 531-567. | Zbl 0737.42018