本文主要是研究关于新近所引进的Besov型和Triebel-izorkin型空间的几个应用.具体地, 本文首先建立了Triebel-izorkin型空间的广义g_λ^*函数的等价刻画,这一刻画本质地改进了经典的Triebel-Lizorkin空间已有的结果;作为应用, 研究了一类满足广义Hörmander条件的Fourier乘子在Triebel-Lizorkin型空间上的有界性.其次, 建立了Besov型空间, Triebel-Lizorkin型空间以及Besov-Morrey空间上的复插值;作为一个简单的推论, 得到了Morrey空间的复插值结果.最后, 本文引进了Musielak-Orlicz Besov型空间和Musielak-Orlicz Triebel-Lizorkin型空间, 建立了它们的φ变换特征并给出了连续特征刻画以及原子、分子分解;这些空间统一了Musielak-Orlicz Hardy空间,加权形式和不加权形式的Besov(型)和Triebel-Lizorkin(型)空间.

This dissertation is mainly devoted to the study ofseveral applications on Besov-type and Triebel-Lizorkin-type spaces.First, we establish a new characterization of Triebel-Lizorkin-type spaces via the generalized g_λ^* function, which essentially improves the known result for Triebel-Lizorkinspaces even when τ=0. Applying this new characterization, we then obtain the boundedness of Fourier multipliers whose symbols satisfy somegeneralized Hörmander condition on Triebel-Lizorkin-type and Triebel-Lizorkin-Hausdorff spaces. Second, we establish the complex interpolation onBesov-type spaces, Triebel-Lizorkin-type spaces and Besov-Morrey spaces. As a corollary, we obtain the complex interpolation for Morrey spaces.Finally, we introduce Musielak-Orlicz Besov-type and Triebel-Lizorkin-type spacesand establish their φ-transform characterizations in the sense of Frazier and Jawerth. Some characterizations via Peetre maximal functions, local means, Lusin area functions, smooth atomic and molecular decompositions of these spaces are also presented.