Embedding Theorems and Area Operators on Bergman Spaces with Doubling Measure

Abstract We establish an embedding theorem for the weighted Bergman spaces induced by a positive Borel measure $$d\omega (y)dx$$ d ω ( y ) x with doubling property $$\omega (0,2t)\le C\omega (0,t)$$ 0 , 2 t ≤ C . The characterization is given in terms of Carleson squares on upper half-plane. As special cases, our result covers standard weights and logarithmic weights. application, we also boundedness area operator.