WIMAN'S INEQUALITY FOR ANALYTIC FUNCTIONS IN D x C WITH RAPIDLY OSCILLATING COEFFICIENTS

Let A(2) be a class of analytic function f represented by power series of the from f (z) = f (z(1), z(2)) = Sigma(+infinity)(n vertical bar m=0) a(nm)z(1)(n) z(2)(m) with the domain of convergence T = {z is an element of C-2 : vertical bar z(1)vertical bar < 1, vertical bar z(2)vertical bar < + infinity} such that partial derivative/partial derivative z(2) f (z(1), z(2)) not equivalent to 0 in T and there exists r(0) = (r(1)(0), r(2)(0)) is an element of [0, 1) x [0, vertical bar infinity) such that for all r is an element of (r(1)(0), 1) x ( r(2)(0), vertical bar infinity) we have r(1) partial derivative/partial derivative r(1) ln Mf (r) + ln r(1) > 1, where Mf (r) = Sigma(+infinity)(n+m=0) vertical bar anm vertical bar r(1)(n)r(2)(m) . Let K(f, theta) = {f (z, t) = Sigma(+infinity)(n+m=0) a(nm)e(2 pi it) (theta(n) +theta(m)) : t is an element of R} be class of analytic functions, where (theta(nm)) is a sequence of positive integer such that its arrangement (theta(*)(k)) by increasing satisfies the condition theta(*)(k+1)/theta(*)(k) >= q > 1, k > 0. For analytic functions from the class K( f, theta) Wiman's inequality is improved.