Cesàro-Like Operators on the Hardy and Bergman Spaces of the Half Plane

Hausdorff operators on holomorphic Hardy spaces and applications

“…A natural question arises is that whether the transformed function H ϕ (f * ) is also the boundary value function of a function in H p a (C + )? In some special cases of ϕ and 1 < p < ∞, using the spectral mapping theorem and the Hille-Yosida-Phillips theorem, Arvanitidis-Siskakis [2] and Ballamoole-Bonyo-Miller-Millerstudied [3] studied and gave affirmative answers to this question.…”

Weighted Composition Groups on the Little Bloch Space

“…To prove the compactness of the resolvent operator, we argue as in [7], eorem 5.2. Fix λ ∈ ρ(Γ 0,1 ) and let m ∈ Z + be such that I(λ) < m. en, by equation (33), it suffices to show that R m (λ,…”

“…In [7], all the self analytic maps (φ t ) t≥0 ⊆ Aut(U) of the upper half-plane U were identified and classified according to the location of their fixed points into three distinct classes, namely, scaling, translation, and rotation groups. For each self-analytic map φ t , we define a corresponding group of weighted composition operator on H(U) by…”

“…It is noted in [7] Section 5 that for the rotation group, we consider the corresponding group of weighted composition operators defined on the analytic spaces of the disc H(D) given by T t f(z) � e ict f e ikt z , with c, k ∈ R, k ≠ 0.…”

“…See, for instance, [3,[8][9][10][11]. In [7,12], both the semigroup and spectral properties of the group (T t ) t∈R were studied in detail on the Hardy and Bergman spaces. e aim of this paper is to extend the analysis of the group (T t ) t∈R from the Hardy and Bergman spaces to the setting of the little Bloch space.…”