Geodesic
Sharp endpoint results for imaginary powers and Riesz transforms on certain noncompact manifolds
Giancarlo Mauceri 1   ; Stefano Meda 2   ; Maria Vallarino 3
1 Dipartimento di Matematica Università di Genova via Dodecaneso 35 16146 Genova, Italy
2 Dipartimento di Matematica e Applicazioni Università di Milano-Bicocca via R. Cozzi 53 I-20125 Milano, Italy
3 Dipartimento di Scienze Matematiche “Giuseppe Luigi Lagrange” Politecnico di Torino corso Duca degli Abruzzi 24 10129 Torino, Italy
Studia Mathematica, Tome 224 (2014) no. 2, pp. 153-168 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $L^1(M)$.
DOI : 10.4064/sm224-2-4
Keywords: consider complete connected noncompact riemannian manifold bounded geometry spectral gap prove imaginary powers laplacian riesz transform bounded hardy space introduced previous work authors

Giancarlo Mauceri  1   ; Stefano Meda  2   ; Maria Vallarino  3

1 Dipartimento di Matematica Università di Genova via Dodecaneso 35 16146 Genova, Italy
2 Dipartimento di Matematica e Applicazioni Università di Milano-Bicocca via R. Cozzi 53 I-20125 Milano, Italy
3 Dipartimento di Scienze Matematiche “Giuseppe Luigi Lagrange” Politecnico di Torino corso Duca degli Abruzzi 24 10129 Torino, Italy 
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     title = {Sharp endpoint results for imaginary powers and {Riesz} transforms on certain noncompact manifolds},
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Giancarlo Mauceri; Stefano Meda; Maria Vallarino. Sharp endpoint results for imaginary powers and Riesz transforms on certain noncompact manifolds. Studia Mathematica, Tome 224 (2014) no. 2, pp. 153-168. doi: 10.4064/sm224-2-4

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