49 research outputs found
Functions in Bloch-type spaces and their moduli
Given a suitably regular nonnegative function on , let
denote the space of all holomorphic functions on the
unit ball of that satisfy with some fixed
. We obtain a new characterization of functions in
terms of their moduli.Comment: 9 pages; to appear in Ann. Acad. Sci. Fenn. Math. 41 (2016), No.
On the singular factor of a linear combination of holomorphic functions
We prove that the linear combinations of functions in
have "few" singular inner factors, provided that the 's are
suitably smooth up to the boundary, while in general this is no longer true.Comment: 4 page
ABC-type estimates via Garsia-type norms
We are concerned with extensions of the Mason--Stothers theorem from
polynomials to analytic functions on the unit disk . The new feature
is that the number of zeros of a function in gets replaced by
the norm of the associated Blaschke product in a suitable smoothness
space . Such extensions are shown to exist, and the appropriate -type
estimates are exhibited, provided that admits a "Garsia-type norm", i.e., a
norm sharing certain properties with the classical Garsia norm on BMO. Special
emphasis is placed on analytic Lipschitz spaces.Comment: 9 page
Remembering Victor Petrovich Havin
These are reminiscences of V. P. Havin (1933--2015), founder of the modern
St. Petersburg analysis school.Comment: 6 pages; to appear in the memorial volume "Tribute to Victor Havin:
50 years with Hardy spaces", Birkh\"auser Verlag, Base