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Award ID contains: 1949206

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  1. ; ; (, Potential Analysis)
    Abstract We characterize the Hilbert–Schmidt class membership of commutator with the Hilbert transform in the two weight setting. The characterization depends upon the symbol of the commutator being in a new weighted Besov space. This follows from a Schatten classSpresult for dyadic paraproducts, where$$1< p < \infty $$ 1 < p < ∞ . We discuss the difficulties in extending the dyadic result to the full range of Schatten classes for the Hilbert transform. 
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  2. ; ; (, Journal of Fourier Analysis and Applications)
    Abstract We study commutators with the Riesz transforms on the Heisenberg group$${\mathbb {H}}^{n}$$ H n . The Schatten norm of these commutators is characterized in terms of Besov norms of the symbol. This generalizes the classical Euclidean results of Peller, Janson–Wolff and Rochberg–Semmes. The method in proof bypasses the use of Fourier analysis, allowing us to address not just the Riesz transforms, but also the Cauchy–Szegő projection and second order Riesz transforms on$${\mathbb {H}}^{n}$$ H n among other settings. 
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    Full Text Available 
  3. ; ; ; (, Banach Journal of Mathematical Analysis)
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  4. ; (, Journal of Mathematical Analysis and Applications)
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  5. ; ; (, Mathematical Research Letters)
    . (Ed.)
    Endpoint Estimates are obtained for the Discrete Prime averages. 
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    Full Text Available 
  6. ; ; (, New York journal of mathematics)
    Accepted Manuscript Full Text Available
  7. ; ; ; ; (, Indiana University Mathematics Journal)
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