This paper gives embedding theorems for a very general class of weighted Bergman spaces: the results include a number of classical Carleson embedding theorems as special cases. The little Hankel operators on these Bergman spaces are also considered. Next, a study is made of Carleson embeddings in the right half-plane induced by taking the Laplace transform of functions defined on the positive h...

We prove generalized Carleson embeddings for the continuous wave packet transform from L p ( R , w ) into an outer space over × 0 ∞ 2 < and weight ∈ A / . This work is a weighted extension of corresponding Lebesgue result in [13] generalizes similar [10] The proof this article relies on restriction estimates which are geometric may be independent interest.

In this note we return on the characterization of the Carleson measures for the class of weighted analytic Besov spaces Bp(ρ) considered in [ARS1], Theorem 1. Since our first paper on this topic, we have found shorter or better proofs for some of the intermediate results, which were used in proving various extensions and generalizations of the characterization theorem, [A][ARS2][ARS3]. Here we ...

Let E ⊂ Rn+1, n ≥ 2, be a uniformly rectifiable set of dimension n. Then bounded harmonic functions in Ω := Rn+1 \ E satisfy Carleson measure estimates, and are “ε-approximable”. Our results may be viewed as generalized versions of the classical F. and M. Riesz theorem, since the estimates that we prove are equivalent, in more topologically friendly settings, to quantitative mutual absolute con...