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Let X be a compact subset of the complex plane ℂ. We denote by R0(X) the algebra consisting of the (restrictions to X of) rational functions with poles off X. Let m denote 2-dimensional Lebesgue measure. For p≥1, let Rp(X) be the closure of R0(X) in Lp(X,dm)

international journal of mathematics and mathematical sciences

Smoothness properties of functions in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$R^2 \left( x \right)$"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>at certain boundary points

Smoothness properties of functions inR2(x)at certain boundary points