The strip problem for Lp functions

2015

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DOI 10.1142/s0129167x15500950
Data confidence 70 medium
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Abstract

Let C be a strictly convex curve in the complex plane whose horizontal translates Ct fill up a strip S ⊆ C. For certain C which are perturbations of an ellipse, we prove that for f in a weighted Lp class on S with p > 2, if f has a holomorphic extension from almost every Ct, then f is holomorphic. The construction works for curves C with no horizontal or vertical symmetry.