In this paper we establish inclusions and noninclusions between various Hardy type spaces on noncompact Riemannian manifolds M with Ricci curvature bounded from below, positive injectivity radius and spectral gap. Our first main result states that, if L is the positive Laplace–Beltrami operator on M, then the Riesz–Hardy space HR1(M) is the isomorphic image of the Goldberg type space h1(M) via the map L1/2(I+L)−1/2, a fact that is false in Rn. Specifically, HR1(M) agrees with the Hardy type space X1/2(M) recently introduced by the first three authors; as a consequence, we prove that HR1(M) does not admit an atomic characterisation. Noninclusions are mostly proved in the special case where the manifold is a Damek–Ricci space S. Our second main result states that HR1(S), the heat Hardy space HH1(S) and the Poisson–Hardy space HP1(S) are mutually distinct spaces, a fact which is in sharp contrast to the Euclidean case, where these three spaces agree.

Martini, A., Meda, S., Vallarino, M., Veronelli, G. (2024). Inclusions and noninclusions of Hardy type spaces on certain nondoubling manifolds. JOURNAL OF FUNCTIONAL ANALYSIS, 286(3 (1 February 2024)) [10.1016/j.jfa.2023.110240].

Inclusions and noninclusions of Hardy type spaces on certain nondoubling manifolds

Meda, S;Veronelli, G
2024

Abstract

In this paper we establish inclusions and noninclusions between various Hardy type spaces on noncompact Riemannian manifolds M with Ricci curvature bounded from below, positive injectivity radius and spectral gap. Our first main result states that, if L is the positive Laplace–Beltrami operator on M, then the Riesz–Hardy space HR1(M) is the isomorphic image of the Goldberg type space h1(M) via the map L1/2(I+L)−1/2, a fact that is false in Rn. Specifically, HR1(M) agrees with the Hardy type space X1/2(M) recently introduced by the first three authors; as a consequence, we prove that HR1(M) does not admit an atomic characterisation. Noninclusions are mostly proved in the special case where the manifold is a Damek–Ricci space S. Our second main result states that HR1(S), the heat Hardy space HH1(S) and the Poisson–Hardy space HP1(S) are mutually distinct spaces, a fact which is in sharp contrast to the Euclidean case, where these three spaces agree.
Articolo in rivista - Articolo scientifico
Exponential growth; Hardy space; Heat semigroup; Maximal function; Noncompact manifold; Poisson semigroup; Riesz transform;
English
9-nov-2023
2024
286
3 (1 February 2024)
110240
none
Martini, A., Meda, S., Vallarino, M., Veronelli, G. (2024). Inclusions and noninclusions of Hardy type spaces on certain nondoubling manifolds. JOURNAL OF FUNCTIONAL ANALYSIS, 286(3 (1 February 2024)) [10.1016/j.jfa.2023.110240].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/455538
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