Necessary Conditions for Fredholmness of Singular Integral Operators with Shifts and Slowly Oscillating Data

Details Necessary Conditions for Fredholmness of Singular Integral Operators with Shifts and Slowly Oscillating Data Necessary Conditions for Fredholmness of Singular Integral Operators with Shifts and Slowly Oscillating Data

2010-10-26

arxiv.org/abs/1010.5336v1

Mathematics

Functional Analysis

26 pages

Scientific paper

Suppose $\alpha$ is an orientation-preserving diffeomorphism (shift) of $\mR_+=(0,\infty)$ onto itself with the only fixed points $0$ and $\infty$. In \cite{KKLsufficiency} we found sufficient conditions for the Fredholmness of the singular integral operator with shift \[ (aI-bW_\alpha)P_++(cI-dW_\alpha)P_- \] acting on $L^p(\mR_+)$ with $1

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