 
Summary: On the boundary behavior of special classes of C1
functions
and analytic functions
J. M. Ash and M. T. Karaev
Abstract. We give a concrete example of a diagonal operator acting in the
Hardy space H2 (D) for which the Berezin symbol has radial limits at no point
of the boundary @D: We use the Berezin symbol technique in the discussion of
several old problems from the classical book of I.I. Privalov [18] related with the
Taylor coe˘ cients and boundary behavior of analytic functions. In particular,
we give in terms of Taylor coe˘ cients
n
bf (n)
o
and Berezin symbols necessary
and su˘ cient conditions ensuring existence of radial boundary values of the
functions f (z) =
P
n 0
bf (n) znfrom the classes lp
A (D) ; 0 < p 1:Lohwater
