Interpolation of operators when the extreme spaces are L

Jesús Bastero; Francisco Ruiz

Studia Mathematica (1993)

  • Volume: 104, Issue: 2, page 133-150
  • ISSN: 0039-3223

Abstract

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Under some assumptions on the pair ( A 0 , B 0 ) , we study equivalence between interpolation properties of linear operators and monotonicity conditions for a pair (Y,Z) of rearrangement invariant quasi-Banach spaces when the extreme spaces of the interpolation are L . Weak and restricted weak intermediate spaces fall within our context. Applications to classical Lorentz and Lorentz-Orlicz spaces are given.

How to cite

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Bastero, Jesús, and Ruiz, Francisco. "Interpolation of operators when the extreme spaces are $L^{∞}$." Studia Mathematica 104.2 (1993): 133-150. <http://eudml.org/doc/215965>.

@article{Bastero1993,
abstract = {Under some assumptions on the pair $(A_0,B_0)$, we study equivalence between interpolation properties of linear operators and monotonicity conditions for a pair (Y,Z) of rearrangement invariant quasi-Banach spaces when the extreme spaces of the interpolation are $L^∞$. Weak and restricted weak intermediate spaces fall within our context. Applications to classical Lorentz and Lorentz-Orlicz spaces are given.},
author = {Bastero, Jesús, Ruiz, Francisco},
journal = {Studia Mathematica},
keywords = {interpolation properties of linear operators; monotonicity conditions; rearrangement invariant quasi-Banach spaces; Lorentz-Orlicz spaces},
language = {eng},
number = {2},
pages = {133-150},
title = {Interpolation of operators when the extreme spaces are $L^\{∞\}$},
url = {http://eudml.org/doc/215965},
volume = {104},
year = {1993},
}

TY - JOUR
AU - Bastero, Jesús
AU - Ruiz, Francisco
TI - Interpolation of operators when the extreme spaces are $L^{∞}$
JO - Studia Mathematica
PY - 1993
VL - 104
IS - 2
SP - 133
EP - 150
AB - Under some assumptions on the pair $(A_0,B_0)$, we study equivalence between interpolation properties of linear operators and monotonicity conditions for a pair (Y,Z) of rearrangement invariant quasi-Banach spaces when the extreme spaces of the interpolation are $L^∞$. Weak and restricted weak intermediate spaces fall within our context. Applications to classical Lorentz and Lorentz-Orlicz spaces are given.
LA - eng
KW - interpolation properties of linear operators; monotonicity conditions; rearrangement invariant quasi-Banach spaces; Lorentz-Orlicz spaces
UR - http://eudml.org/doc/215965
ER -

References

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