| Abstract: | In the fifties, Calderón established a formal relation between symbol and kernel distribution, but it is difficult to establish an intrinsic relation. The Calderón-Zygmund (C-Z) school studied the C-Z operators, and Hörmander, Kohn and Nirenberg, et al. studied the symbolic operators. Here we apply a refinement of the Littlewood-Paley (L-P) decomposition, analyse under new wavelet bases, to characterize both symbolic operators spaces ({text{OP}}S^{m}_{{1,delta }} ) and kernel distributions spaces with other spaces composed of some almost diagonal matrices, then get an isometric between ({text{OP}}S^{m}_{{1,delta }} ) and kernel distribution spaces |
