Martingale transform and L\'evy Processes on Lie Groups

@article{Applebaum2012MartingaleTA,
  title={Martingale transform and L\'evy Processes on Lie Groups},
  author={David Applebaum and Rodrigo Ba{\~n}uelos},
  journal={arXiv: Probability},
  year={2012}
}
This paper constructs a class of martingale transforms based on L\'evy processes on Lie groups. From these, a natural class of bounded linear operators on the $L^p$-spaces of the group (with respect to Haar measure) for $1<p<\infty$, are derived. On compact groups these operators yield Fourier multipliers (in the Peter-Weyl sense) which include the second order Riesz transforms, imaginary powers of the Laplacian, and new classes of multipliers obtained by taking the L\'evy process to have… Expand
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