BMO spaces on domains of R^n
BMO spaces on domains of R^n
Let \(\Omega\) be an open subset of \(\mathbb{R}^n\) and \(\text{MBO}(\Omega)\) denote the space of functions in \(L^1_{\text{loc}}(\overline\Omega)\) with bounded mean oscillation. The authors' main result is that if \(\Omega\) is sufficiently regular, then there is a bounded linear extension operator from \(\text{BMO}_1(\Omega)\) into \(\text{BMO}_1(\mathbb{R}^n)\), where \(\text{BMO}_1(\Omega)\) is somewhat smaller than \(\text{BMO}(\Omega)\). An earlier extension theorem was obtained by \textit{P. W. Jones} [Indiana Univ. Math. J. 29, 41-66 (1980; Zbl 0432.42017)] with a different regularity condition on \(\Omega\) and a different subset of \(\text{BMO}(\Omega)\).
Morrey space, regularity condition, Functions of bounded mean oscillation; Morrey spaces., Banach spaces of continuous, differentiable or analytic functions, bounded mean oscillation, Linear operators on function spaces (general), bounded linear extension operator
Morrey space, regularity condition, Functions of bounded mean oscillation; Morrey spaces., Banach spaces of continuous, differentiable or analytic functions, bounded mean oscillation, Linear operators on function spaces (general), bounded linear extension operator
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