First, some classic properties of a weighted Frobenius-Perron operator on as a predual of weighted Koopman operator on will be investigated using the language of the conditional expectation operator. Also, we determine the spectrum of under certain conditions.
Many problems in analysis are described as weighted norm inequalities that have given rise to different classes of weights, such as -weights of Muckenhoupt and -weights of Ariño and Muckenhoupt. Our purpose is to show that different classes of weights are related by means of composition with classical transforms. A typical example is the family of weights w for which the Hardy transform is -bounded. A -weight is precisely one for which its Hardy transform is in , and also a weight whose indefinite...
We prove some weighted endpoint estimates for some multilinear operators related to certain singular integral operators on Herz and Herz type Hardy spaces.
We consider Bergman projections and some new generalizations of them on weighted -spaces. A new reproducing formula is obtained. We show the boundedness of these projections for a large family of weights v which tend to 0 at the boundary with a polynomial speed. These weights may even be nonradial. For logarithmically decreasing weights bounded projections do not exist. In this case we instead consider the projective description problem for holomorphic inductive limits.