An integral-type operator from bloch spaces to ᵊc_p spaces in the unit ball
نویسندگان
چکیده
منابع مشابه
AN INTEGRAL–TYPE OPERATOR FROM BLOCH SPACES TO Qp SPACES IN THE UNIT BALL
Let H(B) denote the space of all holomorphic functions on the unit ball B of Cn . Let α > 0 , f ∈ H(B) with homogeneous expansion f = ∑k=0 fk . The fractional derivative Dα f is defined as Dα f (z) = ∞ ∑ k=0 (k+1)α fk(z). Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0) = 0 . In this paper we consider the following integral-type operator
متن کاملOn an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball
and Applied Analysis 3 Here H∞ ω denotes the weighted-type space consisting of all f ∈ H B with ∥ ∥f ∥ ∥ H∞ ω sup z∈B ω z ∣ ∣f z ∣ ∣ < ∞ 1.9 see, e.g., 23, 24 . Associated weights assist us in studying of weighted-type spaces of holomorphic functions. It is known that associated weights are also continuous, 0 < ω ≤ ω̃, and for each z ∈ B, we can find an fz ∈ H∞ ω , ‖fz‖H∞ ω ≤ 1 such that fz z 1/...
متن کاملVolterra composition operators from generally weighted Bloch spaces to Bloch-type spaces on the unit ball
Let φ be a holomorphic self-map of the open unit ball B, g ∈ H(B). In this paper, the boundedness and compactness of the Volterra composition operator T g from generally weighted Bloch spaces to Bloch-type spaces are investigated. c ©2012 NGA. All rights reserved.
متن کاملOn an Integral-Type Operator from Zygmund-Type Spaces to Mixed-Norm Spaces on the Unit Ball
and Applied Analysis 3 2. Auxiliary Results In this section, we quote several lemmas which are used in the proofs of the main results. The first lemma was proved in 2 . Lemma 2.1. Assume that φ is a holomorphic self-map of , g ∈ H , and g 0 0. Then, for every f ∈ H it holds [ P g φ ( f )] z f ( φ z ) g z . 2.1 The next Schwartz-type characterization of compactness 28 is proved in a standard way...
متن کاملGeneralized Composition Operator from Bloch–type Spaces to Mixed–norm Space on the Unit Ball
Let H(B) be the space of all holomorphic functions on the unit ball B in CN , and S(B) the collection of all holomorphic self-maps of B . Let φ ∈ S(B) and g ∈ H(B) with g(0) = 0 , the generalized composition operator is defined by C φ ( f )(z) = ∫ 1 0 R f (φ(tz))g(tz) dt t , Here, we characterize the boundedness and compactness of the generalized composition operator acting from Bloch-type spac...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2012
ISSN: 1331-4343
DOI: 10.7153/mia-15-82