Generalized Area Operators on Hardy Spaces

Generalized composition operators on weighted Hardy spaces

On the Generalized Hardy Spaces

and Applied Analysis 3 Definition 2.1. Let F : H U → H U be a linear operator such that F f 0 if and only if f 0, that is, F is 1-1. For 1 ≤ p < ∞, the generalized Hardy space HF,p U HF,p is defined to be the collection of all analytic functions f on U for which

Bilateral composition operators on vector-valued Hardy spaces

Let $T$ be a bounded operator on the Banach space $X$ and $ph$ be an analytic self-map of the unit disk $Bbb{D}$‎. ‎We investigate some operator theoretic properties of‎ ‎bilateral composition operator $C_{ph‎, ‎T}‎: ‎f ri T circ f circ ph$ on the vector-valued Hardy space $H^p(X)$ for $1 leq p leq‎ ‎+infty$.‎ ‎Compactness and weak compactness of $C_{ph‎, ‎T}$ on $H^p(X)$‎ ‎are characterized an...

Bilinear Operators on Herz-type Hardy Spaces

The authors prove that bilinear operators given by finite sums of products of Calderón-Zygmund operators on Rn are bounded from HK̇11 q1 × HK̇ α2,p2 q2 into HK̇ q if and only if they have vanishing moments up to a certain order dictated by the target space. Here HK̇ q are homogeneous Herz-type Hardy spaces with 1/p = 1/p1 +1/p2, 0 < pi ≤ ∞, 1/q = 1/q1 +1/q2, 1 < q1, q2 < ∞, 1 ≤ q < ∞, α = α1 + α2 a...

Multilinear Calderón-zygmund Operators on Hardy Spaces

It is shown that multilinear Calderón-Zygmund operators are bounded on products of Hardy spaces.