In this paper, we define a space h1(M) of Hardy–Goldberg type on a measured metric space satisfying some mild conditions. We prove that the dual of h1(M) may be identified with bmo(M), a space of functions with “local” bounded mean oscillation, and that if p is in (1, 2), then Lp(M) is a complex interpolation space between h1(M) and L2(M). This extends previous results of Strichartz, Carbonaro, Mauceri and Meda, and Taylor. Applications to singular integral operators on Riemannian manifolds are given
Meda, S., Volpi, S. (2017). Spaces of Goldberg type on certain measured metric spaces. ANNALI DI MATEMATICA PURA ED APPLICATA, 196(3), 947-981 [10.1007/s10231-016-0603-6].
Spaces of Goldberg type on certain measured metric spaces
MEDA, STEFANO
Primo
;
2017
Abstract
In this paper, we define a space h1(M) of Hardy–Goldberg type on a measured metric space satisfying some mild conditions. We prove that the dual of h1(M) may be identified with bmo(M), a space of functions with “local” bounded mean oscillation, and that if p is in (1, 2), then Lp(M) is a complex interpolation space between h1(M) and L2(M). This extends previous results of Strichartz, Carbonaro, Mauceri and Meda, and Taylor. Applications to singular integral operators on Riemannian manifolds are given
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