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The Bloch functions and the Bloch space have a long history behind them. They were introduced by the French mathematician André Bloch at the beginning of the last century. Many mathematicians payed attention to these functions: L. Ahlfors, JM Anderson, J. Clunie, Ch. Pommerenke, PL Duren, BW Romberg and AL Shields are some of them. There were some good papers about this topic (see for example [DRS],[ACP]) and in the more recent past the monographs [Z] and [DS].

Our intention is to introduce a concept of Bloch matrix (respectively of Bergman-Schatten matrix) which extends the notion of Bloch function (respectively the function from the Bergman space) and to prove some results generalizing those of the papers [ACP] and [Z]. The idea behind our considerations is to consider an infinite matrix A as the analogue of the formal Fourier series associated to a 2π-periodic distribution, the diagonals Ak, k∈ Z, being the analogues of the Fourier coefficients associated to such a distribution. In this manner we get a one-to-one correspondence between the infinite Toeplitz matrices and formal Fourier series associated to periodic distributions, hence an infinite matrix appears in a natural way as a more general concept than that of a periodic distribution on the