In this paper we raise the question of regularity of the densities $h_t$ of a symmetric stable semigroup ${μ_t}$ of measures on the homogeneous group N under the mere assumption that the densities exist. (For a criterion of the existence of the densities of such semigroups see [11].)
Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
[1] A. P. Calderón and A. Zygmund, On singular integrals, Amer. J. Math. 78 (1956), 289-309.
[2] M. Christ, Hilbert transforms along curves. I. Nilpotent groups, Ann. of Math. 122 (1985), 575-596.
[3] L. Corwin and F. P. Greenleaf, Representations of Nilpotent Lie Groups and Their Applications. Part 1: Basic Theory and Examples, Cambridge University Press, Cambridge, 1990.
[4] M. Duflo, Représentations de semi-groupes de mesures sur un groupe localement compact, Ann. Inst. Fourier (Grenoble) 28 (3) (1978), 225-249.
[5] J. Dziubański and J. Zienkiewicz, Smoothness of densities of semigroups of measures on homogeneous groups, Colloq. Math., to appear.
[6] G. B. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat. 13 (1975), 161-207.
[7] G. B. Folland, Lipschitz classes and Poisson integrals on stratified groups, Studia Math. 66 (1979), 37-55.
[8] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Princeton University Press, Princeton, 1982.
[9] P. Głowacki, Stable semigroups of measures on the Heisenberg group, Studia Math. 79 (1984), 105-138.
[10] P. Głowacki, Stable semi-groups of measures as commutative approximate identities on non- graded homogeneous groups, Invent. Math. 83 (1986), 557-582.
[11] P. Głowacki, The Rockland condition for nondifferential convolution operators, Duke Math. J. 58 (1989), 371-395.
[12] P. Głowacki and W. Hebisch, Pointwise estimates for the densities of stable semigroups of measures, Studia Math. 104 (1993), 243-258.
[13] P. Głowacki and A. Hulanicki, A semi-group of probability measures with non- smooth differentiable densities on a Lie group, Colloq. Math. 51 (1987), 131-139.
[14] B. Helffer et J. Nourrigat, Caractérisation des opérateurs hypoelliptiques homogènes invariants à gauche sur un groupe gradué, Comm. Partial Differential Equations 4 (8) (1979), 899-958.
[15] A. Hulanicki, A class of convolution semi-groups of measures on a Lie group, in: Lecture Notes in Math. 828, Springer, 1980, 82-101.
[16] G. Hunt, Semigroups of measures on Lie groups, Trans. Amer. Math. Soc. 81 (1956), 264-293.
[17] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
[18] E. M. Stein, Boundary behavior of harmonic functions on symmetric spaces: maximal estimates for Poisson integrals, Invent. Math. 74 (1983), 63-83.
[19] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, 1975.
[20] K. Yosida, Functional Analysis, Springer, Berlin, 1980.
[21] F. Zo, A note on approximation of the identity, Studia Math. 55 (1976), 111-122.
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