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Sharp endpoint results for imaginary powers and Riesz transforms on certain noncompact manifolds

Volume 224 / 2014

Giancarlo Mauceri, Stefano Meda, Maria Vallarino 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 $L^1(M)$.


  • Giancarlo MauceriDipartimento di Matematica
    Università di Genova
    via Dodecaneso 35
    16146 Genova, Italy
  • Stefano MedaDipartimento di Matematica e Applicazioni
    Università di Milano-Bicocca
    via R. Cozzi 53
    I-20125 Milano, Italy
  • Maria VallarinoDipartimento di Scienze Matematiche “Giuseppe Luigi Lagrange”
    Politecnico di Torino
    corso Duca degli Abruzzi 24
    10129 Torino, Italy

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