新小波基和象征空间与分布核空间的同构

New Wavelet Bases and Isometry Between Symbolic Operators Spaces OpS_1,δ~m and Kernel Distributions Spaces

虽然在50年代,Calderon就建立了算子的象征和分布核的形式关系,但其内在的联系十分难于建立.本文通过两组新的小波基的一致性,证明象征空间OpS1。

In the fifties, Calderon established a formal relation between symbol and kernel distribution, but it is difficult to. establish an intrinsic relation. The Calderon-Zygmund. (C-Z) school studied the C-Z operators, Hormander, Kohn and Nirenberg et al. studied the symbolic operators. Here we apply a refinement of Littlewood-Paley (L-P) decomposition, analyse under new wavelet bases, to characterize both symbolic operators spaces OpS1,δm and kernel distributions spaces with other spaces composed by some almost diagonal matrix, then one gets an isometric between OpS1,δm and kernel distribution spaces.