- May 27, 2011, Friday - 15h00 (Room P
3.10):
Alexei Karlovich
(Universidade Nova de Lisboa e CEAF, IST)
" On
singular integral operators with semi-almost periodic coefficients on
variable Lebesgue spaces
"
Abstract. Let a be
a semi-almost periodic matrix function with the almost periodic
representatives b and c at minus-infinity and plus-infinity,
respectively. Suppose p(.) is a slowly oscillating exponent such that
the Cauchy singular integral operator S is bounded on the variable
Lebesgue space Lp(.). We prove that if the operator aP+Q with P=(I+S)/2
and Q=(I-S)/2 is Fredholm on the variable Lebesgue space Lp(.), then
the operators bP+Q and cP+Q are invertible on standard Lebesgue spaces
Lq and Lr with some exponents q and r lying in the segments between the
lower and the upper limits of p(.) at minus-infinity and plus-infinity,
respectively. This is a joint work with Ilya Spitkovsky.
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