Sharp endpoint results for imaginary powers and Riesz transforms on certain noncompact manifolds
Tom 224 / 2014
Studia Mathematica 224 (2014), 153-168 MSC: 30H10, 42B20, 42B35, 58C99. DOI: 10.4064/sm224-2-4
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 $X^1(M)$, introduced in previous work of the authors, to $L^1(M)$.