A commutator theorem with applications

• Autores: Mario Milman
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 44, Fasc. 1-3, 1993, págs. 201-210
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We give an extension of the commutator theorems of Jawerth, Rochberg and Weiss [9] for the real method of interpolation. The results are motivated by recentwork by Iwaniec and Sbordone [6] on generalized Hodge decompositions. The main estimates of these authors are based on a commutator theorem for a specific operator acting on $L^p$ spaces and through the use of the complex method of interpolation. In this note we give an extension of the Iwaniec-Sbordone theorem to general real interpolation scales.

• Referencias bibliográficas
  • J. Bergh and J. Löfström, Interpolation Spaces: An introduction, Springer-Verlag, Berlin, Heidelberg and New York, 1976.
  • M. Cwikel, B. Jawerth, and M. Milman, The domain spaces of quasilogarithmic operators, Trans. Amer. Math. Soc. 317 (1990), 599–609.
  • M. Cwikel, B. Jawerth, M. Milman, and R. Rochberg, Differential estimates and commutators in interpolation theory, “Analysis at Urbana II”,...
  • M. Cwikel, N. Kalton, M. Milman, and R. Rochberg, in preparation.
  • F. Feissner, Hypercontractive semigroups and Sobolev’s inequality, Trans. Amer. Math. Soc. 210 (1975), 51–62.
  • T. Iwaniec, and C. Sbordone, Weak minima of variational integrals, University of Naples, preprint 1992.
  • B. Jawerth and M. Milman, New results and applications of extrapolation theory, Interpolation Spaces and Related Topics, M. Cwikel et al editors,...
  • B. Jawerth and M. Milman, Interpolation of weak type spaces, Math. Z. 201 (1989), 509–519.
  • B. Jawerth, R. Rochberg, and G. Weiss, Commutator and other second order estimates in real interpolation theory, Ark. Mat. 24 (1986), 191–219.
  • N. Kalton, Differentials of complex interpolation process for Köthe function spaces, to appear.
  • M. Milman, Extrapolation and Optimal Decompositions with Applications to Analysis, Lecture Notes in Math., Springer, 1994.
  • M. Milman and T. Schonbek, Second order estimates in interpolation theory and applications, Proc. Amer. Math. Soc. 110 (1990), 961–969.
  • R. Rochberg and G. Weiss, Derivatives of analytic families of Banach spaces, Ann. Math. 118 (1983), 315–347.
  • E.M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, 1970.
  • M. Zafran, Spectral theory and interpolation of operators, J. Funct. Anal. 36 (1980), 185–204.