Homeomorphisms acting on Besov and Triebel-Lizorkin spaces of local regularity ps(t)

• Autores: Beatriz Viviani, Silvia I. Hartzstein
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 56, Fasc. 1, 2005, págs. 27-45
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • The aim of this paper is to show that the integral and derivative operators defined by local regularities are homeomorphisms for generalized Besov and TriebelLizorkin spaces with local regularities. The underlying geometry is that of homogeneous type spaces and the functions defining local regularities belong to a larger class of growth functions than the potentials t_, related to classical fractional integral and derivative operators and Besov and TriebelLizorkin spaces.

• Referencias bibliográficas
  • G. David, J.L. Journé, and S. Semmes, Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation, Rev. Mat. Iberoamericana...
  • D.-G. Deng and Y.-S. Han, Calderón type reproducing formula on spaces of homogeneous type, Sci. China Ser. A 38 (1995), 17–28.
  • M. Frazier, B. Jawerth, and G. Weiss, Littlewood-Paley Theory and the Study of Function Spaces, CBMS Regional Conference Series in Mathematics...
  • A.E. Gatto, C. Segovia, and S. Vági, On fractional differentiation and integration on spaces of homogeneous type, Rev. Mat. Iberoamericana...
  • A.E. Gatto and S. Vági, On Sobolev spaces of fractional order and $\epsilon$-families of operators on spaces of homogeneous type, Studia Math....
  • Y.-S. Han and E.T. Sawyer, Littlewood-Paley theory on spaces of homogeneous type and the classical function spaces, Mem. Amer. Math. Soc....
  • S.I. Hartzstein and B.E. Viviani, $T1$ theorems on generalized Besov and Triebel-Lizorkin spaces over spaces of homogeneous type, Rev. Un....
  • S.I. Hartzstein and B.E. Viviani, Integral and derivative operators of functional order on generalized Besov and Triebel-Lizorkin spaces on...
  • S.I. Hartzstein and B.E. Viviani, On the composition of the integral and derivative operators of functional order, Comment. Math. Univ. Carolin....
  • B. Iaffei, Espacios Lipschitz generalizados y operadores invariantes por traslaciones, Thesis, Universidad Nacional del Litoral, Argentina,...
  • R.A. Macías and C. Segovia, Lipschitz functions on spaces of homogeneous type, Adv. in Math. 33 (1979), 257–270.
  • J. Peetre, Sur les espaces de Besov, C. R. Acad. Sci. Paris, Sér. A-B 264 (1967), 281–283.
  • J. Peetre, On spaces of Triebel-Lizorkin type, Ark. Mat. 13 (1975), 123–130.
  • J. Peetre, New Thoughts on Besov Spaces, Duke University Mathematics Series, Durham, NC, 1976.
  • H. Triebel, Theory of Function Spaces, Monographs in Mathematics 78, Birkhäuser Verlag, Basel, 1983.