Paper

{
  "raw_xml": "<entry>\n    <id>http://arxiv.org/abs/2602.24186v1</id>\n    <title>Endpoint Estimates for Bergman Commutators and New Characterizations of the Bloch Space and $H^\\infty$</title>\n    <updated>2026-02-27T17:07:44Z</updated>\n    <link href='https://arxiv.org/abs/2602.24186v1' rel='alternate' type='text/html'/>\n    <link href='https://arxiv.org/pdf/2602.24186v1' rel='related' title='pdf' type='application/pdf'/>\n    <summary>We prove an $\\LlogL $-type distributional inequality for the commutator of the Bergman projection with a conjugate Bloch symbol function on the unit ball. Such an inequality can be seen as a Bergman version of a result due to C. Pérez for real-variable Calderón-Zygmund operators and BMO functions. We also prove that this inequality characterizes membership of analytic functions in the Bloch space and is further equivalent to a kind of modified restricted weak-type estimate, where one only tests over characteristic functions of sets comparable to Bergman balls. We also show our estimate is sharp in the sense that there exists a Bloch function $b$ so that the commutator $[\\bar{b},P]$ is not weak-type $(1,1)$, and prove $[\\bar{b},P]$ with $b$ analytic is weak-type $(1,1)$ if and only if $b \\in H^\\infty$.</summary>\n    <category scheme='http://arxiv.org/schemas/atom' term='math.CV'/>\n    <category scheme='http://arxiv.org/schemas/atom' term='math.FA'/>\n    <published>2026-02-27T17:07:44Z</published>\n    <arxiv:comment>32 pages</arxiv:comment>\n    <arxiv:primary_category term='math.CV'/>\n    <author>\n      <name>Adam B. Christopherson</name>\n    </author>\n    <author>\n      <name>Zhenghui Huo</name>\n    </author>\n    <author>\n      <name>Nathan A. Wagner</name>\n    </author>\n    <author>\n      <name>Yunus E. Zeytuncu</name>\n    </author>\n  </entry>"
}