We consider a complete connected noncompact Riemannian manifold M with bounded geometry and spectral gap. We prove that the imaginary powers of the Laplacian and the Riesz transform are bounded from the Hardy space X1(M), introduced in previous work of the authors, to L1(M).
Mauceri, G., Meda, S., Vallarino, M. (2014). Sharp endpoint estimates for imaginary powers and Riesz transforms on certain noncompact manifolds. STUDIA MATHEMATICA, 224(2), 153-168 [10.4064/sm224-2-4].
Sharp endpoint estimates for imaginary powers and Riesz transforms on certain noncompact manifolds
Meda, S;
2014
Abstract
We consider a complete connected noncompact Riemannian manifold M with bounded geometry and spectral gap. We prove that the imaginary powers of the Laplacian and the Riesz transform are bounded from the Hardy space X1(M), introduced in previous work of the authors, to L1(M).
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