Abstract
AbstractGiven $$E_0, E_1, E, F$$
E
0
,
E
1
,
E
,
F
rearrangement invariant spaces, $$a, \mathrm {b}, \mathrm {b}_0, \mathrm {b}_1$$
a
,
b
,
b
0
,
b
1
slowly varying functions and $$0\le \theta _0<\theta _1\le 1$$
0
≤
θ
0
<
θ
1
≤
1
, we characterize the interpolation spaces $$\begin{aligned} ({\overline{X}}_{\theta _0,\mathrm {b}_0,E_0}, {\overline{X}}^{{\mathcal {R}}}_{\theta _1, \mathrm {b}_1,E_1,a,F})_{\theta ,\mathrm {b},E}\quad \text {and}\quad ({\overline{X}}^{{\mathcal {L}}}_{\theta _0, \mathrm {b}_0,E_0,a,F}, {\overline{X}}_{\theta _1,\mathrm {b}_1,E_1})_{\theta ,\mathrm {b},E}, \end{aligned}$$
(
X
¯
θ
0
,
b
0
,
E
0
,
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¯
θ
1
,
b
1
,
E
1
,
a
,
F
R
)
θ
,
b
,
E
and
(
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¯
θ
0
,
b
0
,
E
0
,
a
,
F
L
,
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¯
θ
1
,
b
1
,
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1
)
θ
,
b
,
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,
for all possible values of $$\theta \in [0,1]$$
θ
∈
[
0
,
1
]
. Applications to interpolation identities for grand and small Lebesgue spaces, Gamma spaces and A and B-type spaces are given.
Funder
Engineering and Physical Sciences Research Council
Ministerio de Economía, Industria y Competitividad, Gobierno de España
Publisher
Springer Science and Business Media LLC