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For a locally compact group G and 1 0, there exists a compact subset K of G such that | | 0, there exists a compact subset K of G such that |u, f| 0 and any compact subset K of G, there exists some f ∈ X with ∥f∥ | > ∥u∥ - ∈. Some results of Flory (1971) and Miao (1999) can be obtained from our main theorems by taking p = 2 and X as some C*-subalgebras of PMp(G).

Characterizations of elements with compact support in the dual spaces of $A_{p}(G)$-modules of $PM_{p}(G)$