• Corpus ID: 16321397

Linear dimension-free estimates for the Hermite-Riesz transforms

@article{Dragivcevic2007LinearDE,
  title={Linear dimension-free estimates for the Hermite-Riesz transforms},
  author={Oliver Dragivcevi'c and Alexander Volberg},
  journal={arXiv: Classical Analysis and ODEs},
  year={2007},
  url={https://api.semanticscholar.org/CorpusID:16321397}
}
We utilize the Bellman function technique to prove a bilinear dimension-free inequality for the Hermite operator. The Bellman technique is applied here to a non-local operator, which at first did not seem to be feasible. As a consequence of our bilinear inequality one proves dimension-free boundedness for the Riesz-Hermite transforms on L^p with linear growth in terms of p. A feature of the proof is a theorem establishing L^p(R^n) estimates for a class of spectral multipliers with bounds… 
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