The Cauchy transform of compactly supported $L^p$ data, $p>2$, is a continuous $W^{1,p}$ solution of the Cauchy–Riemann equation

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The Cauchy transform of compactly supported $L^p$ data, $p>2$, is a continuous $W^{1,p}$ solution of the Cauchy–Riemann equation · Prove2Me