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Description: |
The talk provides a discussion of recent results for the generalized
Lebesgue spaces with variable exponent p(x) (GLSVE) including some
results on boundedness of Hardy-Littlewood maximal operator and
criterion for the weighted singular operator (with a power weight) to be
bounded in such spaces. This result is applied to "localize" the
Gohberg-Krupnik criterion of Fredholmness of singular integral operators
in such spaces on Lyapunov curves. Some abstract Banach space reformulation
of the Gohberg-Krupnik scheme of investigation of Fredholmness is given,
from which the result for GLSVE, in particular follows due to the boundedness
criterion for the weighted singular operator.
Area(s):
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