On the zeros of Bloch functions
A function f, analytic in the unit disc , is said to be a Bloch function if sup z2 (1j zj 2 )jf 0 (z)j <1. In this paper we study the zero sequences of non-trivial Bloch functions. Among other results we prove that if f is a Bloch function with f(0) 0 andfzkg is the sequence of ordered zeros of f; then N Y
We deal with linear parabolic (in the sense ::: of Petrovskii) systems of order $2b$ with discontinuous principal ::: coefficients. A priori estimates in Sobolev and ::: Sobolev--Morrey spaces are proved for the strong solutions by ::: means of potential analysis and boundedness of certain singular ::: integral operators with kernels of mixed homogeneity. As a ::: byproduct, precise characterization of the Morrey, $BMO$ and ::: Holder regularity is given for the solutions and their ::: derivatives up to order $2b-1.$