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Volumn 36, Issue 2, 1998, Pages 201-231

Riesz transforms on compact Lie groups, spheres and Gauss space

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EID: 0010562224     PISSN: 00042080     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02384766     Document Type: Article
Times cited : (33)

References (44)
  • 1
    • 85033884410 scopus 로고
    • Ph. D. Thesis, Washington Univ., St. Louis, Mo.
    • ARCOZZI, N., Ph. D. Thesis, Washington Univ., St. Louis, Mo., 1995.
    • (1995)
    • Arcozzi, N.1
  • 2
    • 0031287209 scopus 로고    scopus 로고
    • Riesz transforms on spheres
    • ARCOZZI, N. and LI, X., Riesz transforms on spheres, Math. Res. Lett. 4 (1997), 401-412.
    • (1997) Math. Res. Lett. , vol.4 , pp. 401-412
    • Arcozzi, N.1    Li, X.2
  • 3
    • 0010965864 scopus 로고
    • 1 sur les sphéres
    • Séminaire de Probabilités XVIII (Azéma, J. and Yor, M., eds.), Springer-Verlag, Berlin-Heidelberg
    • 1 sur les sphéres, in Séminaire de Probabilités XVIII (Azéma, J. and Yor, M., eds.), Lecture Notes in Math. 1059, pp. 197-218, Springer-Verlag, Berlin-Heidelberg, 1984.
    • (1984) Lecture Notes in Math. , vol.1059 , pp. 197-218
    • Bakry, D.1
  • 4
    • 0000389345 scopus 로고
    • Transformations de riesz pour les semigroupes symétriques. I. Étude de la dimension 1
    • Séminaire de Probabilités XIX (Azéma, J. and Yor, M., eds.), Springer-Verlag, Berlin-Heidelberg
    • BAKRY, D., Transformations de Riesz pour les semigroupes symétriques. I. Étude de la dimension 1, in Séminaire de Probabilités XIX (Azéma, J. and Yor, M., eds.), Lecture Notes in Math. 1123, pp. 130-144, Springer-Verlag, Berlin-Heidelberg, 1985.
    • (1985) Lecture Notes in Math. , vol.1123 , pp. 130-144
    • Bakry, D.1
  • 5
    • 0000389345 scopus 로고
    • 2≥0
    • Séminaire de Probabilitiés XIX (Azéma, J. and Yor, M., eds.), Springer-Verlag, Berlin-Heidelberg
    • 2≥0, in Séminaire de Probabilitiés XIX (Azéma, J. and Yor, M., eds.), Lecture Notes in Math. 1123, pp. 145-174, Springer-Verlag, Berlin-Heidelberg, 1985.
    • (1985) Lecture Notes in Math. , vol.1123 , pp. 145-174
    • Bakry, D.1
  • 6
    • 0001017995 scopus 로고
    • Étude des transformées de riesz dans les variétés riemanniennes à courbure de ricci minorée
    • Séminaire de Probabilités XXI (Azéma, J., Meyer, P.-A. and Yor, M., eds.), Springer-Verlag, Berlin-Heidelberg
    • BAKRY D., Étude des transformées de Riesz dans les variétés riemanniennes à courbure de Ricci minorée, in Séminaire de Probabilités XXI (Azéma, J., Meyer, P.-A. and Yor, M., eds.), Lecture Notes in Math. 1247, pp. 137-172, Springer-Verlag, Berlin-Heidelberg, 1987.
    • (1987) Lecture Notes in Math. , vol.1247 , pp. 137-172
    • Bakry, D.1
  • 7
    • 84967791482 scopus 로고
    • Martingale transforms and related singular integrals
    • BAÑUELOS, R., Martingale transforms and related singular integrals, Trans. Amer. Math. Soc. 293 (1986), 547-563.
    • (1986) Trans. Amer. Math. Soc. , vol.293 , pp. 547-563
    • Bañuelos, R.1
  • 9
    • 84974002292 scopus 로고
    • Sharp inequalities for martingales with applications to the Beurling-Ahlfors and Riesz transforms
    • BAÑUELOS, R. and WANG, G., Sharp inequalities for martingales with applications to the Beurling-Ahlfors and Riesz transforms, Duke Math. J. 80 (1995), 575-600.
    • (1995) Duke Math. J. , vol.80 , pp. 575-600
    • Bañuelos, R.1    Wang, G.2
  • 10
    • 84968494618 scopus 로고
    • Probabilistic square functions and a priori estimates
    • BENNETT, A., Probabilistic square functions and a priori estimates, Trans. Amer. Math. Soc. 291 (1985), 159-166.
    • (1985) Trans. Amer. Math. Soc. , vol.291 , pp. 159-166
    • Bennett, A.1
  • 11
    • 85033889818 scopus 로고
    • Ph. D. Thesis, Princeton, N. J.
    • BENNETT A., Ph. D. Thesis, Princeton, N. J., 1985.
    • (1985)
    • Bennett, A.1
  • 12
    • 0001130456 scopus 로고
    • Boundary value problems and sharp inequalities for martingale transforms
    • BURKHOLDER, D. L., Boundary value problems and sharp inequalities for martingale transforms, Ann. Probab. 12 (1984), 647-702.
    • (1984) Ann. Probab. , vol.12 , pp. 647-702
    • Burkholder, D.L.1
  • 13
    • 0002506929 scopus 로고
    • Sharp inequalities for martingales and stochastic integrals
    • BURKHOLDER, D. L., Sharp inequalities for martingales and stochastic integrals, Astérisque 157-158 (1988), 75-94.
    • (1988) Astérisque , vol.157-158 , pp. 75-94
    • Burkholder, D.L.1
  • 14
    • 0001841855 scopus 로고
    • Explorations in martingale theory and its application
    • École d'Été de Probabilités de Saint-Flour XIX - 1989 (Hennequin, P. L., ed.), Springer-Verlag, Berlin-Heidelberg
    • BURKHOLDER, D. L., Explorations in martingale theory and its application, in École d'Été de Probabilités de Saint-Flour XIX - 1989 (Hennequin, P. L., ed.), Lecture Notes in Math. 1464, pp. 1-66, Springer-Verlag, Berlin-Heidelberg, 1991.
    • (1991) Lecture Notes in Math. , vol.1464 , pp. 1-66
    • Burkholder, D.L.1
  • 15
    • 0003326573 scopus 로고
    • Transference methods in analysis
    • Amer. Math. Soc., Providence, R. I.
    • COIFMAN, R. and WEISS, G., Transference Methods in Analysis, CBMS Regional Conf. Ser. in Math. 31, Amer. Math. Soc., Providence, R. I., 1977.
    • (1977) CBMS Regional Conf. Ser. in Math. , vol.31
    • Coifman, R.1    Weiss, G.2
  • 16
    • 51249161264 scopus 로고
    • Isopérimétrie, décroissance du noyau de la chaleur et transformations de riesz: Un contre-exemple
    • COULHON, T. and LEDOUX, M., Isopérimétrie, décroissance du noyau de la chaleur et transformations de Riesz: un contre-exemple, Ark. Mat. 32 (1994), 63-77.
    • (1994) Ark. Mat. , vol.32 , pp. 63-77
    • Coulhon, T.1    Ledoux, M.2
  • 20
    • 0001277724 scopus 로고
    • A superharmonic proof of the M. Riesz conjugate function theorem
    • ESSÉN, M., A superharmonic proof of the M. Riesz conjugate function theorem, Ark. Mat. 22 (1984), 241-249.
    • (1984) Ark. Mat. , vol.22 , pp. 241-249
    • Essén, M.1
  • 22
    • 0002339441 scopus 로고
    • Sur le transformation de riesz pour le sémi-groupe d'ornstein-uhlenbeck
    • GUNDY, R. F., Sur le transformation de Riesz pour le sémi-groupe d'Ornstein-Uhlenbeck, C. R. Acad. Sci. Paris Sér. I Math. 303 (1986), 967-970.
    • (1986) C. R. Acad. Sci. Paris Sér. I Math. , vol.303 , pp. 967-970
    • Gundy, R.F.1
  • 23
    • 0007460230 scopus 로고
    • Some topics in probability and analysis
    • Amer. Math. Soc., Providence, R. I.
    • GUNDY, R. F., Some Topics in Probability and Analysis, CBMS Regional Conf. Ser. in Math. 70, Amer. Math. Soc., Providence, R. I., 1989.
    • (1989) CBMS Regional Conf. Ser. in Math. , vol.70
    • Gundy, R.F.1
  • 24
    • 0010885638 scopus 로고
    • Les transformations de riesz et les intégrales stochastiques
    • GUNDY, R. F. and VAROPOULOS, N., Les transformations de Riesz et les intégrales stochastiques, C. R. Acad. Sci. Paris Sér. A-B 289 (1979), A13-A16.
    • (1979) C. R. Acad. Sci. Paris Sér. A-B , vol.289
    • Gundy, R.F.1    Varopoulos, N.2
  • 26
    • 85026110906 scopus 로고    scopus 로고
    • Riesz transforms and related singular integrals
    • IWANIEC, T. and MARTIN, G., Riesz transforms and related singular integrals, J. Reine Angew. Math. 473 (1996), 25-57.
    • (1996) J. Reine Angew. Math. , vol.473 , pp. 25-57
    • Iwaniec, T.1    Martin, G.2
  • 27
    • 0000869540 scopus 로고
    • Singular integrals in homogeneous spaces and some problems of classical analysis
    • KORÁNYI, A. and VÁGI, S., Singular integrals in homogeneous spaces and some problems of classical analysis, Ann. Scuola Norm. Sup. Pisa 25 (1971), 575-648.
    • (1971) Ann. Scuola Norm. Sup. Pisa , vol.25 , pp. 575-648
    • Korányi, A.1    Vági, S.2
  • 28
    • 0010959536 scopus 로고
    • Group theoretic remarks on Riesz systems on balls
    • KORÁNYI, A. and VÁGI, S., Group theoretic remarks on Riesz systems on balls, Proc. Amer. Math. Soc. 85 (1982), 200-205.
    • (1982) Proc. Amer. Math. Soc. , vol.85 , pp. 200-205
    • Korányi, A.1    Vági, S.2
  • 29
    • 85033891474 scopus 로고
    • Polynômes harmoniques sur un espace gaussien
    • MARTINI, C., Polynômes harmoniques sur un espace gaussien, C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), 419-422.
    • (1995) C. R. Acad. Sci. Paris Sér. I Math. , vol.320 , pp. 419-422
    • Martini, C.1
  • 30
    • 0000422775 scopus 로고
    • Geometry of differential space
    • MCKEAN, H. P., Geometry of differential space, Ann. Probab. 1 (1973), 197-206.
    • (1973) Ann. Probab. , vol.1 , pp. 197-206
    • Mckean, H.P.1
  • 31
    • 0013380799 scopus 로고
    • Démonstrations probabilistes des inégalités de littlewood-paley
    • Séminaire de Probabilités X (Meyer, P.-A., ed.), Springer-Verlag, Berlin Heidelberg
    • MEYER, P.-A., Démonstrations probabilistes des inégalités de Littlewood-Paley, in Séminaire de Probabilités X (Meyer, P.-A., ed.), Lecture Notes in Math. 511, pp. 125-183, Springer-Verlag, Berlin Heidelberg, 1976.
    • (1976) Lecture Notes in Math. , vol.511 , pp. 125-183
    • Meyer, P.-A.1
  • 32
    • 0000113089 scopus 로고
    • Retour sur la théorie de littlewood-paley
    • Séminaire de Probabilités XV (Azéma, J. and Yor, M., eds.), Springer-Verlag, Berlin-Heidelberg
    • MEYER, P.-A., Retour sur la théorie de Littlewood-Paley, in Séminaire de Probabilités XV (Azéma, J. and Yor, M., eds.), Lecture Notes in Math. 850, pp. 151-166, Springer-Verlag, Berlin-Heidelberg, 1981.
    • (1981) Lecture Notes in Math. , vol.850 , pp. 151-166
    • Meyer, P.-A.1
  • 33
    • 0000036412 scopus 로고
    • Transformations de riesz pour les lois gaussiennes
    • Séminaire de Probabilités XVIII (Azéma, J. and Yor, M., eds.), Springer-Verlag, Berlin-Heidelberg
    • MEYER, P.-A., Transformations de Riesz pour les lois gaussiennes, in Séminaire de Probabilités XVIII (Azéma, J. and Yor, M., eds.), Lecture Notes in Math. 1059, pp. 179-193, Springer-Verlag, Berlin-Heidelberg, 1984.
    • (1984) Lecture Notes in Math. , vol.1059 , pp. 179-193
    • Meyer, P.-A.1
  • 34
    • 0000542603 scopus 로고
    • On the best values of the constants in the theorems of M. Riesz, Zygmund and Kolmogorov
    • PICHORIDES, S. K., On the best values of the constants in the theorems of M. Riesz, Zygmund and Kolmogorov, Studia Math. 44 (1972), 165-179.
    • (1972) Studia Math. , vol.44 , pp. 165-179
    • Pichorides, S.K.1
  • 35
    • 0000018741 scopus 로고
    • Riesz transforms: A simple analytic proof of P. A. Meyer's inequality
    • Séminaire de Probabilités XXII (Azéma, J., Meyer, P.-A. and Yor, M., eds.), Springer-Verlag, Berlin-Heidelberg
    • PISIER, G., Riesz transforms: A simple analytic proof of P. A. Meyer's inequality, in Séminaire de Probabilités XXII (Azéma, J., Meyer, P.-A. and Yor, M., eds.), Lecture Notes in Math. 1321, pp. 485-501, Springer-Verlag, Berlin-Heidelberg, 1988.
    • (1988) Lecture Notes in Math. , vol.1321 , pp. 485-501
    • Pisier, G.1
  • 36
    • 0004184360 scopus 로고
    • Elementary functions, Nauka, Moscow, Russian. English transl.: Gordon and Breach, New York
    • PRUDNIKOV, A. P., BRYCHKOV, YU. A. and MARICHEV, O. I., Integrals and Series. Vol. 1. Elementary functions, Nauka, Moscow, 1981 (Russian). English transl.: Gordon and Breach, New York, 1986.
    • (1981) Integrals and Series , vol.1
    • Prudnikov, A.P.1    Brychkov, Y.U.A.2    Marichev, O.I.3
  • 37
    • 0002442253 scopus 로고
    • n-1)
    • Harmonic Analysis in Euclidean Spaces (Weiss, G. and Wainger, S., eds.), Amer. Math. Soc., Providence, R. I.
    • n-1), in Harmonic Analysis in Euclidean Spaces (Weiss, G. and Wainger, S., eds.), Proc. Symp. Pure Math. 35, pp. 289-294, Amer. Math. Soc., Providence, R. I., 1979.
    • (1979) Proc. Symp. Pure Math. , vol.35 , pp. 289-294
    • Ricci, F.1    Weiss, G.2
  • 38
    • 0001964876 scopus 로고
    • Topics in harmonic analysis related to the littlewood-paley theory
    • Princeton Univ. Press, Princeton, N. J.
    • STEIN, E. M., Topics in Harmonic Analysis Related to the Littlewood-Paley Theory, Ann. of Math. Studies 63, Princeton Univ. Press, Princeton, N. J., 1970.
    • (1970) Ann. of Math. Studies , vol.63
    • Stein, E.M.1
  • 40
    • 71249100909 scopus 로고
    • Three variations on the theme of maximal functions
    • Peral, I. and Rubio de Francia, J. L., eds., North-Holland, Amsterdam
    • STEIN, E. M., Three variations on the theme of maximal functions, in Recent Progress in Fourier Analysis (Peral, I. and Rubio de Francia, J. L., eds.), pp. 229-244, North-Holland, Amsterdam, 1985.
    • (1985) Recent Progress in Fourier Analysis , pp. 229-244
    • Stein, E.M.1
  • 42
    • 0040992507 scopus 로고
    • Aspects of probabilistic Littlewood-paley theory
    • VAROPOULOS, N., Aspects of probabilistic Littlewood-Paley theory, J. Funct. Anal. 39 (1980), 25-60.
    • (1980) J. Funct. Anal. , vol.39 , pp. 25-60
    • Varopoulos, N.1
  • 43
    • 0037801439 scopus 로고
    • An estimate of the norm of a function in a Hardy space in terms of the norms of its real and imaginary parts
    • Russian
    • VERBITSKY, I. E., An estimate of the norm of a function in a Hardy space in terms of the norms of its real and imaginary parts, Mat. Issled. 54 (1980), 16-20 (Russian). English transl.: Amer. Math. Soc. Transl. 124 (1984), 11-15.
    • (1980) Mat. Issled. , vol.54 , pp. 16-20
    • Verbitsky, I.E.1
  • 44
    • 0038139089 scopus 로고
    • English transl.
    • VERBITSKY, I. E., An estimate of the norm of a function in a Hardy space in terms of the norms of its real and imaginary parts, Mat. Issled. 54 (1980), 16-20 (Russian). English transl.: Amer. Math. Soc. Transl. 124 (1984), 11-15.
    • (1984) Amer. Math. Soc. Transl. , vol.124 , pp. 11-15


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