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- W3186128019 abstract "In this note, we prove a fractional version in $1$-D of the Bourgain-Brezis inequality cite{bourgain1}. We show that such an inequality is equivalent to the fact that a holomorphic function $fcolonDtoC$ belongs to the Bergman space ${mathcal{A}}^2(D)$, namely $fin L^2(D)$, if and only if $$|f|_{ L^1+ {H}^{-1/2}(S^1)}:=limsup_{rto 1^-}|f(re^{itheta})|_{ L^1+ {H}^{-1/2}(S^1)}<+infty.$$ Possible generalisations to the higher-dimensional torus are explored." @default.
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- W3186128019 date "2021-11-01" @default.
- W3186128019 modified "2023-09-25" @default.
- W3186128019 title "Bergman-Bourgain-Brezis-type inequality" @default.
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- W3186128019 doi "https://doi.org/10.1016/j.jfa.2021.109201" @default.
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