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The trace problem and Hardy operator for non-isotropic function spaces on the Heisenberg group. (English) Zbl 0813.31005
The author proves trace and extension theorems for non-isotropic Sobolev space functions and Besov space functions on the Heisenberg group.

##### MSC:
 31B20 Boundary value and inverse problems for harmonic functions in higher dimensions 43A15 $$L^p$$-spaces and other function spaces on groups, semigroups, etc.
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##### References:
 [1] Aronszajn N., On coercive integro-diffenential forms pp 94– (1955) [2] Aronszajn N., On spaces of potentials connected with L$$sub:p$$esub: classes. 13 pp 211– (1963) [3] Besov, O. 1961.Investigation of a family of function spaces in connection with theorems of imbeddings and extensions, Vol. 60, 42–81. Steklov: Trudy Mat. Inst. Amer. Math. Soc. Translations ser.2,40(1964),161–207 [4] Folland G., Estimates for the bcomplex and analysis on the Heisenberg group. 27 pp 429– (1974) [5] Folland G., Subelliptic estimates and function spaces on milpotent Lie group 13 pp 161– (1975) [6] Gagliardo, E. 1957.Caratheizzazione delle trace sulla frontiera relative ad aleune classi di funziora in n variabili, Vol. 27, 284–305. Padova: Rend. Sem. Mat. Univ. M.R. 21, 1525 · Zbl 0087.10902 [7] Jerison D., The Dirichlet problem for the Kohn Laplacian on the Heisenberg group. 43 pp 284– (1987) [8] Hörmander L., Hypoelliptic second order differential equations 119 pp 147– (1967) · Zbl 0156.10701 [9] Krantz S., Analysis on the Heisenberg group and estimates for functions in Hardy classes of several complex variables 244 pp 243– (1979) · Zbl 0401.43004 [10] DOI: 10.1007/BF02392539 · Zbl 0578.32044 · doi:10.1007/BF02392539 [11] Nagel A., Estimates for the Bergman and Szegö kernels in Cp:2 129 pp 113– (1989) [12] Pesenson, I. 1979.On Interpolation Spaces on Lie Groups, Vol. 246, 1298–1303. Dokl. Acad. Nauk SSSR. Trans.:Sovit Math. Dokl 28(1989),113-149 [13] Pesenson, I. 1983.The Nikol’skii-Besov spaces Connected with Representations of Lic Groups, Vol. 273, 45–49. Dokl. Akad. Nauk SSSR. Transl.: Soviet Math. Dokl. 28 (1983).577-581 [14] Pesenson, I. 1990.Functions which are smooth along vector fields, Vol. 48, 95–104. Mat. Zametki. Transl.: Notes of the Aczdemy of Sciences of the USSR, 3 (1901). 683-688 [15] Rothschild L., Hypoelliptic differential operators and nilpotent groups 137 pp 247– (1976) [16] Seeley R., Extension of C functions defined in half-space 15 pp 625– (1964) · Zbl 0127.28403 [17] Slobodeckii, L. 1958.Sobolev’s spaces of fractional order and their application to boundary problems for partial differential equations, Vol. 118, 243–246. Russian: Dokl. Akad. Nauk SSSR. M.R. 21,5059 [18] Stein E., The characterization of functions arising as potentials. I 67 pp 102– (1961) [19] Triebel H., Interpolation theory (1978) · Zbl 0387.46033 [20] Varopoulos N., Analysis on Lie groups 76 pp 346– (1988)
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