{"paper":{"title":"Hardy spaces and the Szeg\\H{o} projection of the non-smooth worm domain $D'_\\beta$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Alessandro Monguzzi","submitted_at":"2015-04-01T16:44:03Z","abstract_excerpt":"We define Hardy spaces $H^p(D'_\\beta)$ on the non-smooth worm domain $D'_\\beta=\\{(z_1,z_2)\\in\\mathbb{C}^2:|Im z_1-\\log |z_2|^2|<\\frac{\\pi}{2}, |\\log |z_2|^2|<\\beta-\\frac{\\pi}{2}\\}$ and we prove a series of related results such as the existence of boundary values on the distinguished boundary $\\partial D'_\\beta$ of the domain and a Fatou-type theorem (i.e. pointwise convergence to the boundary values). Thus, we study the Szeg\\H{o} projection operator $\\widetilde{S}$ and the associated Szeg\\H{o} kernel $K_{D'_\\beta}$. More precisely, if $H^p(\\partial D'_\\beta)$ denotes the space of functions whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00287","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}