# Extreme cases of weak type interpolation.

Revista Matemática Iberoamericana (2005)

- Volume: 21, Issue: 2, page 557-576
- ISSN: 0213-2230

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topPustylnik, 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 -

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