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Regularity of solutions of the tangential Cauchy-Riemann (CR) equation is shown on domains in Levi-flat CR manifolds for the class of C∞ forms up to the boundary. These domains are transversal intersections of the CR submanifold with pseudoconvex domains with piecewise smooth boundary.

kyushu journal of mathematics

&lt;i&gt;C&lt;/i&gt;&lt;sup&gt;&amp;infin;&lt;/sup&gt;-REGULARITY OF THE TANGENTIAL CAUCHY-RIEMANN EQUATIONS ON LEVI-FLAT SUBMANIFOLDS OF C&lt;sup&gt;&lt;i&gt;n&lt;/sup&gt;&lt;/i&gt;