Ukrainian mathematical congress  2009
Yuriy Karlovych (Universidad Autónoma del Estado de Morelos, Morelos, Mexico) WienerHopf operators with oscillating matrix symbols on weighted Lebesgue spaces We establish Fredholm criteria for WienerHopf operators $W(a)$ with oscillating matrix symbols $a$, continuous on the real line $R$ and admitting mixed (slowly oscillating and semialmost periodic) discontinuities at $\pm\infty$, on weighted Lebesgue spaces $L^p_N(R_+,w)$ where $1< p < \infty$, $N=1,2,\ldots$, and $w$ belongs to a subclass of Muckenhoupt weights. For $N>1$ these criteria are conditional. To obtain these results we apply the techniques of limit operators and use the theory of WienerHopf operators with semialmost periodic matrix symbols and slowly oscillating matrix symbols on weighted Lebesgue spaces elaborated by us earlier on the basis of the theory of pseudodifferential and Calder\'onZygmund operators, results on oscillating Fourier multipliers and factorization of almost periodic matrix functions. The talk is based on a joint work with Juan Loreto Hern\'andez.
