Extrapolation theory for the real interpolation method

• Autores: Joaquín Martín, María Jesús Carro Rossell
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 53, Fasc. 2, 2002, págs. 165-186
• Idioma: inglés
• Títulos paralelos:
  • Teoría de extrapolación para el método de interpolación real
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• Resumen

  • We develop an abstract extrapolation theory for the real interpolation method that covers and improves the most recent versions of the celebrated theorems of Yano and Zygmund. As a consequence of our method, we give new endpoint estimates of the embedding Sobolev theorem for an arbitrary domain Omega.

• Referencias bibliográficas
  • Copilot said: C. Bennett and R. Sharpley, Interpolation of operators, Academic Press, Boston, 1988.
  • J. Bergh and J. Löfström, Interpolation spaces, An introduction, Springer, New York, 1976.
  • Yu.A. Brudnyi and N. Ya. Krugljak, Interpolation functors and interpolation spaces, North-Holland, Amsterdam, 1991.
  • M.J. Carro, On the range space of Yano’s extrapolation theorems and new extrapolation estimates at $p=\infty$, Preprint 2000.
  • M.J. Carro, New extrapolation estimates, J. Funct. Anal. 174 (2000), 155–166.
  • M.J. Carro and J. Martín, On embedding properties of some extrapolation spaces, Preprint 2000.
  • R. DeVore and K. Scherer, Interpolation of linear operators on Sobolev spaces, Ann. of Math. 109 (1979), 583–609.
  • D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin-New York, 1977.
  • B. Jawerth and M. Milman, Extrapolation theory with applications, Mem. Amer. Math. Soc. 89, 1991.
  • B. Jawerth and M. Milman, New results and applications of extrapolation theory, Interpolation spaces and related topics (Haifa, 1990), 81–105,...
  • M. Milman, Extrapolation and optimal decompositions with applications to analysis, Lecture Notes in Math. 1580, Springer-Verlag, Berlin, 1994.
  • E.M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series 30, Princeton University Press,...
  • E.C. Titchmarsh, Additional note on conjugate functions, J. London Math. Soc. 4 (1929), 204–206.
  • S. Yano, An extrapolation theorem, J. Math. Soc. Japan 3 (1951), 296–305.
  • A. Zygmund, Trigonometric series, Cambridge University Press, New York, 1959.