• Corpus ID: 117264557

Sharp Lower bound estimates for vector-valued and matrix-valued multipliers in $L^p$

@article{Boros2011SharpLB,
  title={Sharp Lower bound estimates for vector-valued and matrix-valued multipliers in \$L^p\$},
  author={Nicholas Boros and Alexander Volberg},
  journal={arXiv: Classical Analysis and ODEs},
  year={2011}
}

• N. Boros, A. Volberg
• Published 25 October 2011
• Mathematics
• arXiv: Classical Analysis and ODEs

We generalize the idea of a multiplier in two different ways and generalize a recent result of Geiss, Montomery-Smith and Saksman. First of all, we consider multipliers in the form of a vector acting on a scalar function. Using this technique we compute the sharp lower bound estimate for $L^p$ operator norm of a quadratic perturbation of the real part of the Ahlfors-Beurling operator. Secondly, we consider matrix-valued multipliers to obtain a new proof showing that the $L^p$ operator norm of the Ahlfors-Beurling operator is bounded below by p^*-1.