Extreme cases of weak type interpolation.

Pustylnik, Evgeniy. "Extreme cases of weak type interpolation.." Revista Matemática Iberoamericana 21.2 (2005): 557-576. <http://eudml.org/doc/41943>.

@article{Pustylnik2005,
abstract = {We consider quasilinear operators T of joint weak type (a, b; p, q) (in the sense of [2]) and study their properties on spaces Lφ,E with the norm||φ(t) f*(t)||Ê, where Ê is arbitrary rearrangement-invariant space with respect to the measure dt/t. A space Lφ,E is said to be "close" to one of the endpoints of interpolation if the corresponding Boyd index of this space is equal to 1/a or to 1/p. For all possible kinds of such "closeness", we give sharp estimates for the function ψ(t) so as to obtain that every T: Lφ,E → Lψ,E.},
author = {Pustylnik, Evgeniy},
journal = {Revista Matemática Iberoamericana},
keywords = {Espacios de funciones medibles; Interpolación; Operadores lineales; rearrangement invariant spaces; Boyd indices; weak interpolation},
language = {eng},
number = {2},
pages = {557-576},
title = {Extreme cases of weak type interpolation.},
url = {http://eudml.org/doc/41943},
volume = {21},
year = {2005},
}

TY - JOUR
AU - Pustylnik, Evgeniy
TI - Extreme cases of weak type interpolation.
JO - Revista Matemática Iberoamericana
PY - 2005
VL - 21
IS - 2
SP - 557
EP - 576
AB - We consider quasilinear operators T of joint weak type (a, b; p, q) (in the sense of [2]) and study their properties on spaces Lφ,E with the norm||φ(t) f*(t)||Ê, where Ê is arbitrary rearrangement-invariant space with respect to the measure dt/t. A space Lφ,E is said to be "close" to one of the endpoints of interpolation if the corresponding Boyd index of this space is equal to 1/a or to 1/p. For all possible kinds of such "closeness", we give sharp estimates for the function ψ(t) so as to obtain that every T: Lφ,E → Lψ,E.
LA - eng
KW - Espacios de funciones medibles; Interpolación; Operadores lineales; rearrangement invariant spaces; Boyd indices; weak interpolation
UR - http://eudml.org/doc/41943
ER -