Abstract
AbstractRelative weakly compact sets and weak convergence in variable exponent Lebesgue spaces $${L^{p(\cdot )}(\Omega )}$$
L
p
(
·
)
(
Ω
)
for infinite measure spaces $$(\Omega ,\mu )$$
(
Ω
,
μ
)
are characterized. Criteria recently obtained in [14] for finite measures are here extended to the infinite measure case. In particular, it is showed that the inclusions between variable exponent Lebesgue spaces for infinite measures are never L-weakly compact. A lattice isometric representation of $${L^{p(\cdot )}(\Omega )}$$
L
p
(
·
)
(
Ω
)
as a variable exponent space $$L^{q(\cdot )}(0,1)$$
L
q
(
·
)
(
0
,
1
)
is given.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis
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