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Duals of homogeneous weighted sequence Besov spaces and applications

Huang P.-K., Wang K.

Journal of Applied Analysis

2011

Vol. 17, nr 2

181-205

In this article, we study the duals of homogeneous weighted sequence Besov spaces b α,q p,w, where the weight w is non-negative and locally integrable. In particular, when 0 < p < 1, we find a type of new sequence spaces which characterize the duals of b α,q p,w. Also, we find the necessary and sufficient conditions for the boundedness of diagonal matrices acting on homogeneous weighted sequence Besov spaces. 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 Ap weight.