Let H be a compact subgroup of a locally compact group G. We consider the homogeneous space G/H equipped with a strongly quasi-invariant Radon measure μ. For 1 ≤ p ≤ +∞, we introduce a norm decreasing linear map from Lp(G) onto Lp(G/H, μ) and show that Lp(G/H, μ) may be identified with a quotient space of Lp(G). Also, we prove that Lp(G/H, μ) is isometrically isomorphic to a closed subspace of Lp(G). These help us study the structure of the classical Banach spaces constructed on a homogeneous space via those created on topological groups.
AUTHOR KEYWORDS: Classical Banach space; Homogeneous space; Locally compact topological group; Strongly quasi-invariant measure PUBLISHER: Duke University Press
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