The aim of this paper is to show that the integral and derivative operators defined by local regularities are homeomorphisms for generalized Besov and Triebel-Lizorkin 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 tα, related to classical fractional integral and derivative operators and Besov and Triebel-Lizorkin spaces.
@article{urn:eudml:doc:41819,
title = {Homeomorphisms acting on Besov and Triebel-Lizorkin spaces of local regularity $\psi$(t).},
journal = {Collectanea Mathematica},
volume = {56},
year = {2005},
pages = {27-45},
zbl = {1099.42014},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41819}
}
Hartzstein, Silvia I.; Viviani, Beatriz E. Homeomorphisms acting on Besov and Triebel-Lizorkin spaces of local regularity ψ(t).. Collectanea Mathematica, Tome 56 (2005) pp. 27-45. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41819/