From Diophantine Approximations to Tangential Fatou Property

<div class="line" id="line-5"> The classical Littlewood&rsquo;s counter-example to the tangential Fatou theorem is based on a Diophantine approximation estimate due to Khintchine. This result of Littlewood initiated studies of the boundary behavior of harmonic and analytic functions along various approach paths.</div><div class="line" id="line-28"> <br/></div><div class="line" id="line-21"> We consider bounded harmonic and analytic functions de&filig;ned on the unit disc and study their boundary behavior along tangential approach region whose shape may change from point to point. We prove sharpness of Shon&rsquo;s tangential approach regions and solve a problem posed by W.Rudin in 1979 thus completing the picture given by the classical theorems of Fatou (1906), Lindeloef (1915), Littlewood (1927), and Nagel&amp; Stein (1984).</div><div class="line" id="line-34"> <br/></div><div class="line" id="line-23"> The talk is based on two articles, one joint with Fausto di Biase, Olof Svensson, Tomasz Weiss, and the other with Kathryn Hare.</div>