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More generally, we show that for $q\\in [1,\\infty)$, these Banach algebras can be represented on an $L^q$-space if and only if one of the following holds: (a) $p=2$ and $G$ is abelian; or (b) $|\\frac 1p - \\frac 12|=|\\frac 1q - \\frac 12|$. This result can be interpreted as follows: for $p,q\\in [1,\\infty)$, the $L^p$- and $"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.08612","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-27T15:40:05Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"95b8aef7ff7ffec50ef858ce4d5c1aabada3f84f68676d8e1a4bbf79855994e7","abstract_canon_sha256":"335773502f70bdfc874c2879202a4cbe14352ab365bd2ea4403fb1301e5b815b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:49.389925Z","signature_b64":"WDK8p5X4CDQWktKJmb7B60f/nFdAoBu6z5VI7ae61BKSa3QcT+kNPWspMxki6AFFmP6sS8LOGsmpOiMO4AB3BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d2bcf3e295ffb1d52a192c14a6e7abc27e2ad6947d6812b1c08e72e9d947f21","last_reissued_at":"2026-05-17T23:47:49.389492Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:49.389492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Representations of $p$-convolution algebras on $L^q$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Eusebio Gardella, Hannes Thiel","submitted_at":"2016-09-27T15:40:05Z","abstract_excerpt":"For a nontrivial locally compact group $G$, and $p\\in [1,\\infty)$, consider the Banach algebras of $p$-pseudofunctions, $p$-pseudomeasures, $p$-convolvers, and the full group $L^p$-operator algebra. 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