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Let E be a compact subset of the complex plane ℂ. We denote by R(E) the algebra consisting of (the restrictions to E of) rational functions with poles off E. Let m denote 2-dimensional Lebesgue measure. For p≥1, let Rp(E) be the closure of R(E) in Lp(E,dm)

international journal of mathematics and mathematical sciences

Functions in the space<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$R^2 \left( E \right)$"><mml:msup><mml:mi>R</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>E</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>at boundary points of the interior

Functions in the spaceR2(E)at boundary points of the interior