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On the smoothness of eigenfunctions of hyponormal singular integral operators

On the smoothness of eigenfunctions of hyponormal singular integral operators

Fix <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi element-of upper L Superscript normal infinity Baseline left-parenthesis upper E right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>φ<!-- φ --></mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi mathvariant="normal">∞<!-- ∞ --></mml:mi> </mml:msup> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>E</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\varphi \in {L^\infty }(E)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and …