On conjugate Poisson integrals and Riesz transforms for the Hermite expansions

• Autorzy: S. Thangavelu
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1993
• Tom: 64
• Numer: 1
• Strony: 103-113

Daty

wydano

1993

otrzymano

1991-04-08

poprawiono

1992-01-15

Twórcy

autor

S. Thangavelu

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

Bibliografia

• [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.