Essential Norms of Weighted Composition Operators between Hardy Spaces in the Unit Ball
نویسنده
چکیده
Let φ(z) = (φ1(z), · · · , φn(z)) be a holomorphic self-map of Bn and ψ(z) a holomorphic function on Bn, and H(Bn) the class of all holomorphic functions on Bn, where Bn is the unit ball of C , the weight composition operator Wψ,φ is defined by Wψ,φ = ψf(φ) for f ∈ H(Bn). In this paper we estimate the essential norm for the weighted composition operator Wψ,φ acting from the Hardy space H to H (0 < p, q ≤ ∞). When p = ∞ and q = 2, we give an exact formula for the essential norm. As their applications, we also obtain some sufficient and necessary conditions for the bounded weighted composition operator to be compact from H to H.
منابع مشابه
Essential norm estimates of generalized weighted composition operators into weighted type spaces
Weighted composition operators appear in the study of dynamical systems and also in characterizing isometries of some classes of Banach spaces. One of the most important generalizations of weighted composition operators, are generalized weighted composition operators which in special cases of their inducing functions give different types of well-known operators like: weighted composition operat...
متن کاملWeighted composition operators on weighted Bergman spaces and weighted Bloch spaces
In this paper, we characterize the bonudedness and compactness of weighted composition operators from weighted Bergman spaces to weighted Bloch spaces. Also, we investigate weighted composition operators on weighted Bergman spaces and extend the obtained results in the unit ball of $mathbb{C}^n$.
متن کاملGeneralized Weighted Composition Operators From Logarithmic Bloch Type Spaces to $ n $'th Weighted Type Spaces
Let $ mathcal{H}(mathbb{D}) $ denote the space of analytic functions on the open unit disc $mathbb{D}$. For a weight $mu$ and a nonnegative integer $n$, the $n$'th weighted type space $ mathcal{W}_mu ^{(n)} $ is the space of all $fin mathcal{H}(mathbb{D}) $ such that $sup_{zin mathbb{D}}mu(z)left|f^{(n)}(z)right|begin{align*}left|f right|_{mathcal{W}_...
متن کاملEssential norm of generalized composition operators from weighted Dirichlet or Bloch type spaces to Q_K type spaces
In this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted Dirichlet spaces or Bloch type spaces to $Q_K$ type spaces.
متن کاملWeighted composition operators between weighted Bergman spaces and Hardy spaces on the unit ball of C
In this paper, we study the weighted composition operators Wφ,ψ :f → ψ(f ◦ φ) between weighted Bergman spaces and Hardy spaces on the unit ball of Cn. We characterize the boundedness and the compactness of the weighted composition operators Wφ,ψ :Ap(να)→Aq(νβ) (0 < q < p <∞, −1 < α,β <∞) and Wφ,ψ :Hp(B)→Hq(B) (0 < q < p <∞). © 2006 Elsevier Inc. All rights reserved.
متن کامل