Functional Analysis and Applications Seminar 

16/09/2011, 15:00 — 16:00 — Room P3.10, Mathematics Building
Yuri Karlovich, Universidad Autónoma del Estado de Morelos, México

Algebras of convolution type operators with oscillating data

Let ${B}_{p,w}$ denote the Banach algebra of all bounded linear  operators acting on the weighted Lebesgue space $L^p(\mathbb{R},w)$ where  $1 \lt p \lt \infty$ 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 $a\mathcal{F}^{-1}b\mathcal{F}$  where $\mathcal{F}$ is the Fourier transform, the functions $a, b\in L^\infty (\mathbb{R})$ admit piecewise slowly oscillating discontinuities on  $\mathbb{R}\cup\{\infty\}$ and $b$ is a Fourier multiplier on $L^p(\mathbb{R},w)$. 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 $A\in {A}_{p,w}$ in  terms of their Fredholm symbols.

The talk is based on a joint work with I. Loreto Hernández.