Table des matières de ce fascicule | Article précédent | Article suivant
Shiferaw Berhanu; Jorge Hounie
Traces and the F. and M. Riesz theorem for vector fields
(Traces et théorème de F. et M. Riesz pour les champs de vecteurs)
Annales de l'institut Fourier, 53 no. 5 (2003), p. 1425-1460
Article PDF | Analyses MR 2032939 | Zbl 1037.35024
Class. Math.: 35F15, 35B30, 42B30, 42A38, 30E25
Mots clés: valeurs faiblement bornées, champs de vecteurs intégrables localement, espaces de Hardy, propriété de F. et M. Riesz
Nous étudions dans ce travail des conditions qui assurent l'existence de valeurs au bord
pour des solutions faibles d'un champ de vecteurs complexe différentiable, dans le plan.
Nous donnons des applications à la propriété de F. et M. Riesz pour les champs de
vecteurs.
[BT] M.S. Baouendi & F. Treves, “A property of the functions and distributions annihilated by a locally integrable system of complex vector fields”, Ann. of Math 113 (1981), p. 387-421 MR 607899 | Zbl 0491.35036
[BK] K. Barbey & H. Konig, Abstract analytic function theory and Hardy algebras, Lecture Notes in Math 593, Springer, 1977 MR 442690 | Zbl 0373.46062
[BH1] S. Berhanu & J. Hounie, “An F. and M. Riesz theorem for planar vector fields”, Math. Ann 320 (2001), p. 463-485 MR 1846773 | Zbl 0984.35045
[BH2] S. Berhanu & J. Hounie, “On boundary properties of solutions of complex vector fields”, J. Funct. Anal 192 (2002), p. 446-490 MR 1923410 | Zbl 1011.35142
[B] R.G.M. Brummelhuis, “A microlocal F. and M. Riesz theorem with applications”, Revista Matematica Iberoamericana 5 (1989), p. 21-36 MR 1057336 | Zbl 0714.58055
[Du] P. Duren, Theory of $H^p$ spaces, Academic Press, 1970 MR 268655 | Zbl 0215.20203
[Hö] L. Hörmander, The analysis of linear partial differential operators I, Springer-Verlag, 1990 Zbl 0712.35001
[K1] S. Koshi, Topics in complex analysis: Recent developments on the F. and M. Riesz theorem, Polish Acad. Sci. 31, Banach Center Publ, 1995 MR 1341391 | Zbl 0830.43011
[K2] S. Koshi, The F. and M. Riesz theorem on locally compact abelian groups, 1996, p. 138-145 Zbl 0852.43003
[N] L. Nirenberg, Lectures on linear partial differential equations, Reg. Conf. Series in Math. 17, Amer. Math.Soc, 1973 MR 450755 | Zbl 0267.35001
[NT] L. Nirenberg & F. Treves, “Solvability of a first order linear partial differential equation”, Comm. Pure Appl. Math 16 (1963), p. 331-351 MR 163045 | Zbl 0117.06104
[RS1] J.-P. Rosay & E.L. Stout, “Strong boundary values, analytic functionals and nonlinear Paley-Wiener theory”, Memoirs of the AMS 153 (2001) MR 1846591 | Zbl 0988.46032
[RS2] J.-P. Rosay & E.L. Stout, “Strong boundary values: independence of the defining function and spaces of test functions”, Ann. Sc. Norm. Sup. Pisa, to appear, 2002 MR 1994800 | Zbl 1051.46026
[T] F. Treves, Hypo-analytic structures, local theory, Princeton University Press, 1992 MR 1200459 | Zbl 0787.35003
Shiferaw Berhanu; Jorge Hounie
Traces and the F. and M. Riesz theorem for vector fields
(Traces et théorème de F. et M. Riesz pour les champs de vecteurs)
Annales de l'institut Fourier, 53 no. 5 (2003), p. 1425-1460
Article PDF | Analyses MR 2032939 | Zbl 1037.35024
Class. Math.: 35F15, 35B30, 42B30, 42A38, 30E25
Mots clés: valeurs faiblement bornées, champs de vecteurs intégrables localement, espaces de Hardy, propriété de F. et M. Riesz
Résumé - Abstract
Bibliographie
[BK] K. Barbey & H. Konig, Abstract analytic function theory and Hardy algebras, Lecture Notes in Math 593, Springer, 1977 MR 442690 | Zbl 0373.46062
[BH1] S. Berhanu & J. Hounie, “An F. and M. Riesz theorem for planar vector fields”, Math. Ann 320 (2001), p. 463-485 MR 1846773 | Zbl 0984.35045
[BH2] S. Berhanu & J. Hounie, “On boundary properties of solutions of complex vector fields”, J. Funct. Anal 192 (2002), p. 446-490 MR 1923410 | Zbl 1011.35142
[B] R.G.M. Brummelhuis, “A microlocal F. and M. Riesz theorem with applications”, Revista Matematica Iberoamericana 5 (1989), p. 21-36 MR 1057336 | Zbl 0714.58055
[Du] P. Duren, Theory of $H^p$ spaces, Academic Press, 1970 MR 268655 | Zbl 0215.20203
[Hö] L. Hörmander, The analysis of linear partial differential operators I, Springer-Verlag, 1990 Zbl 0712.35001
[K1] S. Koshi, Topics in complex analysis: Recent developments on the F. and M. Riesz theorem, Polish Acad. Sci. 31, Banach Center Publ, 1995 MR 1341391 | Zbl 0830.43011
[K2] S. Koshi, The F. and M. Riesz theorem on locally compact abelian groups, 1996, p. 138-145 Zbl 0852.43003
[N] L. Nirenberg, Lectures on linear partial differential equations, Reg. Conf. Series in Math. 17, Amer. Math.Soc, 1973 MR 450755 | Zbl 0267.35001
[NT] L. Nirenberg & F. Treves, “Solvability of a first order linear partial differential equation”, Comm. Pure Appl. Math 16 (1963), p. 331-351 MR 163045 | Zbl 0117.06104
[RS1] J.-P. Rosay & E.L. Stout, “Strong boundary values, analytic functionals and nonlinear Paley-Wiener theory”, Memoirs of the AMS 153 (2001) MR 1846591 | Zbl 0988.46032
[RS2] J.-P. Rosay & E.L. Stout, “Strong boundary values: independence of the defining function and spaces of test functions”, Ann. Sc. Norm. Sup. Pisa, to appear, 2002 MR 1994800 | Zbl 1051.46026
[T] F. Treves, Hypo-analytic structures, local theory, Princeton University Press, 1992 MR 1200459 | Zbl 0787.35003
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