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Verbitsky, Stephen Quinn","submitted_at":"2017-02-09T02:30:04Z","abstract_excerpt":"We study the weighted norm inequality of $(1,q)$-type,\n  \\[ \\Vert \\mathbf{G}\\nu \\Vert_{L^q(\\Omega, d\\sigma)} \\le C \\Vert \\nu \\Vert, \\quad \\text{ for all } \\nu \\in \\mathcal{M}^+(\\Omega), \\] along with its weak-type analogue, for $0 < q < 1$, where $\\mathbf{G}$ is an integral operator associated with the nonnegative kernel $G(x,y)$. 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