no. 5
Traces and the F. and M. Riesz theorem for vector fields
Berhanu, Shiferaw1; Hounie, Jorge2
1 Temple University, Department of Mathematics, Philadelphia PA 19122-6094 (USA)
2 UFSCar, Departamento de Matemática, 13565.905 São Carlos SP (Brazil)
Annales de l'Institut Fourier, Volume 53 (2003) no. 5, pp. 1425-1460.

This work studies conditions that insure the existence of weak boundary values for solutions of a complex, planar, smooth vector field L. Applications to the F. and M. Riesz property for vector fields are discussed.

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.

DOI: 10.5802/aif.1984
Classification: 35F15, 35B30, 42B30, 42A38, 30E25
Keywords: weak boundary values, locally integrable vector fields, Hardy spaces, F. and M. Riesz property
Mot clés : valeurs faiblement bornées, champs de vecteurs intégrables localement, espaces de Hardy, propriété de F. et M. Riesz
Berhanu, Shiferaw 1; Hounie, Jorge 2

1 Temple University, Department of Mathematics, Philadelphia PA 19122-6094 (USA)
2 UFSCar, Departamento de Matemática, 13565.905 São Carlos SP (Brazil) 
@article{AIF_2003__53_5_1425_0,
     author = {Berhanu, Shiferaw and Hounie, Jorge},
     title = {Traces and the {F.} and {M.} {Riesz} theorem for vector fields},
     journal = {Annales de l'Institut Fourier},
     pages = {1425--1460},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {53},
     number = {5},
     year = {2003},
     doi = {10.5802/aif.1984},
     zbl = {1037.35024},
     mrnumber = {2032939},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1984/}
}
TY  - JOUR
AU  - Berhanu, Shiferaw
AU  - Hounie, Jorge
TI  - Traces and the F. and M. Riesz theorem for vector fields
JO  - Annales de l'Institut Fourier
PY  - 2003
SP  - 1425
EP  - 1460
VL  - 53
IS  - 5
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1984/
DO  - 10.5802/aif.1984
LA  - en
ID  - AIF_2003__53_5_1425_0
ER  - 
%0 Journal Article
%A Berhanu, Shiferaw
%A Hounie, Jorge
%T Traces and the F. and M. Riesz theorem for vector fields
%J Annales de l'Institut Fourier
%D 2003
%P 1425-1460
%V 53
%N 5
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1984/
%R 10.5802/aif.1984
%G en
%F AIF_2003__53_5_1425_0
Berhanu, Shiferaw; Hounie, Jorge. Traces and the F. and M. Riesz theorem for vector fields. Annales de l'Institut Fourier, Volume 53 (2003) no. 5, pp. 1425-1460. doi : 10.5802/aif.1984. https://aif.centre-mersenne.org/articles/10.5802/aif.1984/

[B] R.G.M. Brummelhuis A microlocal F. and M. Riesz theorem with applications, Revista Matematica Iberoamericana, Volume 5 (1989), pp. 21-36 | MR | Zbl

[BH1] S. Berhanu; J. Hounie An F. and M. Riesz theorem for planar vector fields, Math. Ann, Volume 320 (2001), pp. 463-485 | DOI | MR | Zbl

[BH2] S. Berhanu; J. Hounie On boundary properties of solutions of complex vector fields, J. Funct. Anal, Volume 192 (2002), pp. 446-490 | DOI | MR | Zbl

[BK] K. Barbey; H. Konig Abstract analytic function theory and Hardy algebras, Lecture Notes in Math, 593, Springer, Berlin, 1977 | MR | Zbl

[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, Volume 113 (1981), pp. 387-421 | DOI | MR | Zbl

[Du] P. Duren Theory of H p spaces, Academic Press, 1970 | MR | Zbl

[Hö] L. Hörmander The analysis of linear partial differential operators I, Springer-Verlag, 1990 | Zbl

[K1] S. Koshi Topics in complex analysis: Recent developments on the F. and M. Riesz theorem, Polish Acad. Sci., 31, Banach Center Publ, Warsaw, 1995 | MR | Zbl

[K2] S. Koshi The F. and M. Riesz theorem on locally compact abelian groups, Infinite-dimensional harmonic analysis (Tubingen, 1995) (1996), pp. 138-145 | Zbl

[N] L. Nirenberg Lectures on linear partial differential equations, Reg. Conf. Series in Math., 17, Amer. Math.Soc, 1973 | MR | Zbl

[NT] L. Nirenberg; F. Treves Solvability of a first order linear partial differential equation, Comm. Pure Appl. Math, Volume 16 (1963), pp. 331-351 | DOI | MR | Zbl

[RS1] J.-P. Rosay; E.L. Stout Strong boundary values, analytic functionals and nonlinear Paley-Wiener theory, Memoirs of the AMS, Volume 153 (2001) no. 725 | MR | Zbl

[RS2] J.-P. Rosay; E.L. Stout Strong boundary values: independence of the defining function and spaces of test functions (2002) (Ann. Sc. Norm. Sup. Pisa, to appear) | Numdam | MR | Zbl

[T] F. Treves Hypo-analytic structures, local theory, Princeton University Press, 1992 | MR | Zbl

Cited by Sources: