Traces and the F. and M. Riesz theorem for vector fields

Shiferaw Berhanu[1]; Jorge Hounie[2]

  • [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 (2003)

  • Volume: 53, Issue: 5, page 1425-1460
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Berhanu, Shiferaw, and Hounie, Jorge. "Traces and the F. and M. Riesz theorem for vector fields." Annales de l’institut Fourier 53.5 (2003): 1425-1460. <http://eudml.org/doc/116077>.

@article{Berhanu2003,
abstract = {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.},
affiliation = {Temple University, Department of Mathematics, Philadelphia PA 19122-6094 (USA); UFSCar, Departamento de Matemática, 13565.905 São Carlos SP (Brazil)},
author = {Berhanu, Shiferaw, Hounie, Jorge},
journal = {Annales de l’institut Fourier},
keywords = {weak boundary values; locally integrable vector fields; Hardy spaces; F. and M. Riesz property},
language = {eng},
number = {5},
pages = {1425-1460},
publisher = {Association des Annales de l'Institut Fourier},
title = {Traces and the F. and M. Riesz theorem for vector fields},
url = {http://eudml.org/doc/116077},
volume = {53},
year = {2003},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 5
SP - 1425
EP - 1460
AB - 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.
LA - eng
KW - weak boundary values; locally integrable vector fields; Hardy spaces; F. and M. Riesz property
UR - http://eudml.org/doc/116077
ER -

References

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  1. 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), 387-421 Zbl0491.35036MR607899
  2. K. Barbey, H. Konig, Abstract analytic function theory and Hardy algebras, 593 (1977), Springer, Berlin Zbl0373.46062MR442690
  3. S. Berhanu, J. Hounie, An F. and M. Riesz theorem for planar vector fields, Math. Ann 320 (2001), 463-485 Zbl0984.35045MR1846773
  4. S. Berhanu, J. Hounie, On boundary properties of solutions of complex vector fields, J. Funct. Anal 192 (2002), 446-490 Zbl1011.35142MR1923410
  5. R.G.M. Brummelhuis, A microlocal F. and M. Riesz theorem with applications, Revista Matematica Iberoamericana 5 (1989), 21-36 Zbl0714.58055MR1057336
  6. P. Duren, Theory of H p spaces, (1970), Academic Press Zbl0215.20203MR268655
  7. L. Hörmander, The analysis of linear partial differential operators I, (1990), Springer-Verlag Zbl0712.35001
  8. S. Koshi, Topics in complex analysis: Recent developments on the F. and M. Riesz theorem, 31 (1995), Banach Center Publ, Warsaw Zbl0830.43011MR1341391
  9. S. Koshi, The F. and M. Riesz theorem on locally compact abelian groups, Infinite-dimensional harmonic analysis (Tubingen, 1995) (1996), 138-145 Zbl0852.43003
  10. L. Nirenberg, Lectures on linear partial differential equations, 17 (1973), Amer. Math.Soc Zbl0267.35001MR450755
  11. L. Nirenberg, F. Treves, Solvability of a first order linear partial differential equation, Comm. Pure Appl. Math 16 (1963), 331-351 Zbl0117.06104MR163045
  12. J.-P. Rosay, E.L. Stout, Strong boundary values, analytic functionals and nonlinear Paley-Wiener theory, Memoirs of the AMS 153 (2001) Zbl0988.46032MR1846591
  13. J.-P. Rosay, E.L. Stout, Strong boundary values: independence of the defining function and spaces of test functions, (2002) Zbl1051.46026MR1994800
  14. F. Treves, Hypo-analytic structures, local theory, (1992), Princeton University Press Zbl0787.35003MR1200459

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