Characterizations Of Bergman-orlicz Spaces And Their Applications

The dissertation is devoted to the characterizations of Bergman-Orlicz type spaces and their applications.The plan is the following:Firstly,we present the characterizations of Bergman-Musielak-Orlicz spaces via derivative.Then we obtain the interpolation of Bergman-Musielak-Orlicz spaces and the boundedness of the extended cesàro operator in Bergman-Musielak-Orlicz spaces.Secondly,we give characterizations for Bergman-Orlicz spaces on the unit disk with standard weights in terms of Lipschitz type conditions in the Euclidean,hyperbolic and pseudo-hyperbolic metrics.As a application,we obtain the boundedness of symmetry lifting operators from Bergman-Orlicz spaces on the unit disk into Bergman-Orlicz spaces on the bidisk.Then we generalize those characterizations for Bergman-Orlicz spaces on higher dimension spaces.Finally,we give characterizations for harmonic Bergman-Orlicz spaces with standard weights in terms of Lipschitz type conditions in the Euclidean,hyperbolic,and pseudo-hyperbolic metrics on the half-spaces.And we obtain the boundedness of a difference quotient of harmonic functions on the halfspace.