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Kim, Elena ; Ogden, W. Jacob ; Reerink, Tommie ; Zeytuncu, Yunus E. ( , New York journal of mathematics)The complex Green operator $\mathcal{G}$ on CR manifolds is the inverse of the Kohn-Laplacian $\square_b$ on the orthogonal complement of its kernel. In this note, we prove Schatten and Sobolev estimates for $\mathcal{G}$ on the unit sphere $\mathbb{S}^{2n-1}\subset \mathbb{C}^n$. We obtain these estimates by using the spectrum of $\boxb$ and the asymptotics of the eigenvalues of the usual Laplace-Beltrami operator.more » « less
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Ahn, John ; Bansil, Mohit ; Brown, Garrett ; Cardin, Emilee ; Zeytuncu, Yunus E. ( , Involve, a Journal of Mathematics)
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Abbas, Tawfik ; Brown, Madelyne M. ; Ramasami, Allison ; Zeytuncu, Yunus E. ( , Involve, a Journal of Mathematics)