On Tangential and Projectively Adjacent Approach Regions
Fausto Di Biase; Haguma Gratien; Olof Svensson · 2025 · arXiv
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Abstract (excerpt)
In 1906 Fatou proved that bounded holomorphic functions on the unit disc converge a.e. on the boundary along nontangential approach regions. In 1927 Littlewood proved a negative result, i.e., that a.e. convergence fails for certain approach regions: More precisely, it fails for the rotationally invariant families of tangential approach regions that end curvilinearly at the boundary. The fact that tangential approach regions which end sequentially at the boundary may instead be very well conducive to a.e. convergence was understood more recently by W. Rudin (in 1979) and A. Nagel and E.M. Stein
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Metadata source: arXiv