Atomic Decomposition of Weighted Besov Spaces

We find the atomic decomposition of functions in the weighted Besov spaces under certain factorization conditions on the weight. Introduction. After achieving the atomic decomposition of Hardy spaces (see [8,22, 33]), many of the function saces have been shown to admit similar decompositions. Let us mention the decomposition of B.M.O. (see [32, 25]), Bergman spaces (see [9, 23]), the predual of Bloch space (see [ 11]), Besov spaces (see [15, 4, 10]), Lipschitz spaces (see [18]), Triebel-Lizorkin spaces (see [16, 31]),... They are obtained by quite different methods, but there is a unified and beautiful approach to get the decomposition for most of the spaces. This is the use of a formula du…