SOME OPERATORS ACTING ON WEIGHTED SEQUENCE BESOV SPACES AND APPLICATIONS

In this article, we study the boundedness of matrix operators acting on weighted sequence Besov spaces (b) over dot(p,w)(alpha,q). First we obtain the necessary and sufficient condition for the boundedness of diagonal matrices acting on weighted sequence Besov space (b) over dot(p,w)(alpha,q) and investigate the duals of (b) over dot(p,w)(alpha,q) where the weight is non-negative and locally integrable. In particular, when 0 < p < 1, we find a type of new sequence sapces which characterize the dual space of (b) over dot(p,w)(alpha,q). We also use the duals of (b) over dot(p,w)(alpha,q) to characterize an algebra of matrix operators acting on weighted sequence Besov spaces (b) over dot(p,w)(alpha,q) and find the necessary and sufficient conditions to such a characterization. Note that we do not require that the given weight satisfies the doubling condition in this situation. Using these results, we give some applications to characterize the boundedness of Fourier-Haar multipliers and paraproduct operators. In this situation, we need to require that the weight w is an A(p) weight.