Volterra Type Operators On Derivative Hardy Spaces And Weighted Banach Spaces

This paper studies two aspects regarding the Volterra type operators:on some specific function spaces with respect to boundedness,compactness and invariant subspaces and so forth.On the one hand,this paper studies the boundedness and compactness of T_g and S_goperators on derivative Hardy spaces S~p and weighted Banach spaces H_μ~∞.Firstly,the conditions for the boundedness and compactness of T_g and S_g operators on S~p spaces are given,and in the meantime,the spectra of these operators are investigated.Then,the related problems of the spectra and isometries of the multiplicative operators M_g induced by T_g and S_g operators on S~P spaces are considered.Secondly,when T_g and S_g operators satisfy certain conditions,this paper completely characterizes the boundedness and compactness of T_g and S_g operators on H_μ~∞ spaces with arbitrary weights μ,and also investigates the related problems on Bloch type spaces associated with H_μ~∞ spaces.On the other hand,this paper first studies the problems of the invariant subspaces of T_g and S_g operators on S~P spaces.Next,with the characterizations for algebraic structures of the shift operators M_z on S~P spaces,the invariant subspaces of M_z+nT_z operators on the Hardy spaces H~p are discussed.Finally,this paper poses a conjecture about the invariant subspaces of M_z+nT_z operators on Hardy spacesH1.