Essential norm estimate of a composition operator between Bloch-type spaces in the unit ball
نویسندگان
چکیده
منابع مشابه
Generalized 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...
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Let U be the unit polydisc of C n and φ = (φ1, . . . , φn) a holomorphic self-map of U. By Bp(Un), B 0 (U) and B 0∗ (U) denote the p-Bloch space, Little p-Bloch space and Little star p-Bloch space in the unit polydisc U respectively, where p, q > 0. This paper gives the estimates of the essential norms of bounded composition operators Cφ induced by φ between Bp(Un) (B 0(Un) or B 0∗(Un) ) and Bq...
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For p > 0, let B(Bn) and Lp(Bn) respectively denote the p-Bloch and holomorphic p-Lipschitz spaces of the open unit ball Bn in C . It is known that B(Bn) and L1−p(Bn) are equal as sets when p ∈ (0, 1). We prove that these spaces are additionally norm-equivalent, thus extending known results for n = 1 and the polydisk. As an application, we generalize work by Madigan on the disk by investigating...
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Let U be the unit polydisc of C n and φ = (φ1, . . . , φn) a holomorphic selfmap of U. By Bp(Un), B 0 (U) and B 0∗ (U) denote the p-Bloch space, Little p-Bloch space and Little star p-Bloch space in the unit polydisc U respectively, where p, q > 0. This paper gives the estimates of the essential norms of bounded composition operators Cφ induced by φ between Bp(Un) (B 0(Un) or B 0∗ (U) ) and Bq(...
متن کاملThe Essential Norm of Composition Operator between Generalized Bloch Spaces in Polydiscs and its Applications
Let U be the unit polydisc of C n and φ = (φ1, . . . , φn) a holomorphic self-map of U. By Bp(Un), B 0 (U) and B 0∗ (U) denote the p-Bloch space, Little p-Bloch space and Little star p-Bloch space in the unit polydisc U respectively, where p, q > 0. This paper gives the estimates of the essential norms of bounded composition operators Cφ induced by φ between Bp(Un) (B 0(Un) or B 0∗(Un) ) and Bq...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2012
ISSN: 0035-7596
DOI: 10.1216/rmj-2012-42-3-1049