{"paper":{"title":"On generalized Toeplitz and little Hankel operators on Bergman spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jani Virtanen, Jari Taskinen","submitted_at":"2017-03-29T06:17:17Z","abstract_excerpt":"We find a concrete integral formula for the class of generalized Toeplitz operators $T_a$ in Bergman spaces $A^p$, $1<p<\\infty$, studied in an earlier work by the authors. The result is extended to little Hankel operators. We give an example of an $L^2$-symbol $a$ such that $T_{|a|} $ fails to be bounded in $A^2$, although $T_a : A^2 \\to A^2$ is seen to be bounded by using the generalized definition. We also confirm that the generalized definition coincides with the classical one whenever the latter makes sense."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09896","kind":"arxiv","version":1},"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"}