分形Cauchy空间到Bloch型空间的复合算子与微分算子乘积的范数估计

Essential Norm of Products of Composition and Differentiation between the Fractional Cauchy Spaces and the Bloch Spaces

对分形Cauchy空间到Bloch型空间的复合算子C_(φ)与微分算子乘积D C_(φ)、C_(φ)D进行研究,对算子D C_(φ):F_(α)→B^(β)、C_(φ)D:F_(α)→B^(β)的本性范数给出了新的估计,并对算子D C_(φ):F_(α)→B^(β)、C_(φ)D:F_(α)→B^(β)的有界性、紧性以及本性范数给出新的刻画.

In this paper,we study DCφand C_(φ)D,the products of composition operator Cφand differentiation operator from the fractal Cauchy spaces to the Bloch spaces,and give some new estimates for the essential norms of the operators DCφ:Fα→B^(β),CφD:Fα→B^(β).Moreover,we give a new characterization of the boundedness,compactness and essential norms of the operators DCφ:Fα→B^(β),CφD:Fα→B^(β).