- September 16,
2011, Friday - 15h00 (Room
P
3.10):
Yuri Karlovich
(Universidad Autónoma del Estado de Morelos, México)
" Algebras of
convolution type operators with oscillating data "
Abstract. Let B_{p,w} denote the Banach
algebra of all bounded linear operators acting on the weighted Lebesgue
space L^p (R,w) where
1<p<\infty and w is in a subclass of Muckenhoupt weights.
We
study the Banach subalgebra A_{p,w} of B_{p,w} generated by
all
convolution type operators of the form a F^{-1}b F where F
is the
Fourier transform, the functions a, b belong to L^\infty (R) admit
piecewise slowly oscillating discontinuities on the one point
compactification of the real line and b is a Fourier multiplier on L^p
(R,w). Applying results on commutators of pseudodifferential operators
with non-regular symbols, the Allan-Douglas local principle and the
limit operators techniques, we construct a Fredholm symbol calculus and
obtain a Fredholm criterion for the operators in A_{p,w} in terms
of
their Fredholm symbols.
The talk is based on a joint work with I. Loreto
Hernández.
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