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1993 | 66 | 1 | 29-47
Tytuł artykułu

Lipschitz continuity of densities of stable semigroups of measures

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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].)
Słowa kluczowe
Rocznik
Tom
66
Numer
1
Strony
29-47
Opis fizyczny
Daty
wydano
1993
otrzymano
1993-01-05
Twórcy
  • 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv66i1p29bwm
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