×

zbMATH — the first resource for mathematics

Boundary behavior of harmonic functions on symmetric spaces: maximal estimates for Poisson integrals. (English) Zbl 0522.43007

MSC:
43A85 Harmonic analysis on homogeneous spaces
22E30 Analysis on real and complex Lie groups
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Berline, N., Vergne, M.: Equations de Hua et noyau de Poisson. Lecture Notes in Mathematics, vol. 880, pp. 1-51. Berlin-Heidelberg-New York: Springer 1981 · Zbl 0521.32024
[2] Bernstein, I.N., Gelfand, S.I.: Meromorphic property of the functionsp ?. Funk. Anal.3, 84-85 (1969)
[3] Bochner, S.: Group invariance of Cauchy’s formula in several variables. Ann. of Math.45, 686-707 (1944) · Zbl 0060.24301 · doi:10.2307/1969297
[4] Cordoba, A.: Maximal functions, covering lemmas and Fourier multipliers. Proc. Symp. Pure Math. Amer. Math. Soc.35, 29-49 (1979) · Zbl 0472.42010
[5] Fefferman, R.: A theory of entropy in Fourier analysis. Advances in Math.30, 171-201 (1978) · Zbl 0441.42019 · doi:10.1016/0001-8708(78)90036-1
[6] Furstenberg, H.: A Poisson formula for semi-simple Lie groups. Ann. of Math.77, 335-386 (1963) · Zbl 0192.12704 · doi:10.2307/1970220
[7] Folland, G.B., Stein, E.M.: Hardy spaces on homogenous groups. Mathematical notes, vol. 28. Princeton: Princeton University Press 1982 · Zbl 0508.42025
[8] Gindikin, S.G., Karpalevich, F.I.: Plancherel measure for Riemann symmetric spaces of nonpositive curvature. Dokl. Akad. Nauk SSSR145, 252-255 (1962)
[9] harish-Chandra, L.: Spherical functions on a semi-simple Lie group, I. Amer. Journ. of Math.80, 241-310 (1958) · Zbl 0093.12801 · doi:10.2307/2372786
[10] Helgason, S.: Differential geometry and symmetric spaces. New York: Academic Press 1962 · Zbl 0111.18101
[11] Helgason, S., Koranyi, A.: A Fatou-type theorem for harmonic functions on symmetric spaces. Bull. Amer. Math. Soc.74, 258-263 (1968) · Zbl 0153.42902 · doi:10.1090/S0002-9904-1968-11912-3
[12] Hua, L.K.: Harmonic analysis of functions of several complex variables in the classical domains. Amer. Math. Soc., Providence, (1963) · Zbl 0112.07402
[13] Jessen, B., marcinkiewicz, J., Zygmund, A.: Note on the differentiability of multiple integrals. Fund. Math.25, 217-234 (1935) · Zbl 0012.05901
[14] Johnson, K.: Differential equations and the Bergman-Shilov boundary on the Siegel upper-half plane. Arkiv fur Mat.16, 95-108 (1978) · Zbl 0395.22013 · doi:10.1007/BF02385985
[15] Johnson, K., Koranyi, A.: The Hua operators on bounded symmetric domains of tube type. Annals of Math.111, 589-608 (1980) · Zbl 0468.32007 · doi:10.2307/1971111
[16] Knapp, A.: Fatou’s theorem for symmetric spaces, I. Annals of Math.88, 106-127 (1968) · Zbl 0157.42403 · doi:10.2307/1970557
[17] Knapp, A., Williamson, R.E.: Poisson integrals and semi-simple groups. J. Analyse Math.24, 53-76 (1971) · Zbl 0247.31002 · doi:10.1007/BF02790369
[18] Koranyi, A.: harmonic functions on Hermitian hyperbolic spaces. Trans. Amer. Math. Soc.135, 507-516 (1969) · Zbl 0174.38801
[19] Koranyi, A.: Harmonic functions on symmetric spaces. In: Symmetric spaces, Bothby and Weiss (eds.). New York: M. Dekker 1972 · Zbl 0291.43016
[20] Koranyi, A.: Boundary behavior of Poisson integrals on symmetric spaces. Trans. Amer. Math. Soc.140, 393-409 (1969) · Zbl 0179.15103
[21] Koranyi, A.: Compactification of symmetric spaces and harmonic functions. Lecture Notes, vol. 739, pp. 341-365. Berlin-Heidelberg-New York: Springer 1979 · Zbl 0425.43014
[22] Koranyi, A., Vagi, I.: Singular integrals in homogeneous spaces and some problems of classical analysis. Ann. Scuola Norm. Sup. Pisa,25, 575-648 (1971) · Zbl 0291.43014
[23] Lindahl, L.A.: Fatou’s theorem for symmetric spaces. Ark. for Mat.10, 33-47 (1972) · Zbl 0246.22010 · doi:10.1007/BF02384800
[24] Marcinkiewicz, J., Zygmund, A.: On the summability of double Fourier series. Fund. Math.32, 112-132 (1939) · JFM 65.0266.01
[25] Moore, C.: Compactifications of symmetric spaces I, II. Amer. Jour. Math.86, 201-218, 358-378 (1964) · Zbl 0156.03202 · doi:10.2307/2373040
[26] Nagel, A., riviere, N., Wainger, S.: A maximal function associated to the curve (t, t 2). Proc. Natl. Acad. Sci. (USA)73, 1416-1417 (1976) · Zbl 0325.43009 · doi:10.1073/pnas.73.5.1416
[27] Satake, I.: On representations and compactifications of symmetric Riemannian spaces. Ann. of Math.71, 77-110 (1960) · Zbl 0094.34603 · doi:10.2307/1969880
[28] Stein, E.M.: The analogues of Fatou’s theorem and estimates for maximal functions, in C.I.M.E., Course on geometry of bounded homogeneous domains, pp. 291-307. Roma: Cremonese 1968
[29] Stein, E.M.: Some problems in harmonic analysis suggested by symmetric spaces and semi-simple groups. Proc. Inter. Congress Math. NiceI, 173-189 (1970)
[30] Stein, E.M.: Singular integrals and differentiability properties of functions. Princeton: Princeton University Press 1970 · Zbl 0207.13501
[31] Stein, E.M.: Maximal functions. Proc. Natl. Acad. Sci. (USA)73, 2176-2177, 2547-2549 (1976) · Zbl 0332.42019 · doi:10.1073/pnas.73.7.2176
[32] Stein, E.M., Wainger, S.: Problems in harmonic analysis related to curvature. Bull. Amer. Math. Soc.84, 1239-1295 (1978) · Zbl 0393.42010 · doi:10.1090/S0002-9904-1978-14554-6
[33] Stein, E.M., Weiss, G.: Introduction to Fourier analysis on Euclidean spaces. Princeton: Princeton University Press 1971 · Zbl 0232.42007
[34] Stein, E.M., Weiss, N.J.: On the convergence of Poisson integrals. Trans. Amer. Math. Soc.140, 35-54 (1969) · Zbl 0182.10801 · doi:10.1090/S0002-9947-1969-0241685-X
[35] Zo, F.: A note on approximation of the identity. Studia Math.55, 111-122 (1977) · Zbl 0326.44005
[36] Zygmund, A.: Trigonometric series. Cambridge: Cambridge Univ. Press 1959 · Zbl 0085.05601
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.