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We generalize this result to all Besov spaces $B_p$ with $0<p\\le1$ and all Lipschitz spaces $\\Lambda_t$ with $t>1$. We also obtain a version for Bergman and Fock spaces."},"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":"1101.2995","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-01-15T16:00:50Z","cross_cats_sorted":[],"title_canon_sha256":"59a5f9d290e93f0e9d0bc527bdda541a053ddba88b1cbac0df102091b2cf9a9c","abstract_canon_sha256":"3156908f46defcb00fffec8f39258b34f6cc1c68596380720641441518bcefba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:19.508480Z","signature_b64":"QzXj5AMO9VUB08RT6qhX1HBuwU0+7Vd/lLD1eAZt3F8y+Zj5cZWRBstnA7osUrPbyJeOhTir6FOSC9/v7oQ1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"367c8486425fcc6f4d03a83a659f0636de66d1681f568126e102f2ddce9da4e4","last_reissued_at":"2026-05-17T23:53:19.507937Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:19.507937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An integral representation for Besov and Lipschitz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Kehe Zhu","submitted_at":"2011-01-15T16:00:50Z","abstract_excerpt":"It is well known that functions in the analytic Besov space $B_1$ on the unit disk $\\D$ admits an integral representation $$f(z)=\\ind\\frac{z-w}{1-z\\bar w}\\,d\\mu(w),$$ where $\\mu$ is a complex Borel measure with $|\\mu|(\\D)<\\infty$. We generalize this result to all Besov spaces $B_p$ with $0<p\\le1$ and all Lipschitz spaces $\\Lambda_t$ with $t>1$. 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