AbstractLet 0⩽α<∞, 0<p<∞, and p−α>−2. If f is holomorphic in the unit disc D and if ω is a radial weight function of secure type, then the followings are equivalent:∫D|f(z)|pω(z)dA(z)<∞,∫D|f(z)|p−α|∇˜f(z)|αω(z)dA(z)<∞,∫01(∫02π|f(reiθ)|pdθ)1−α/p(∫02π|∇˜f(reiθ)|pdθ)α/pω(r)rdr<∞. Here ∇˜f(z)=(1−|z|2)f′(z). Furthermore, if f(0)=0 and ω is monotone, then three quantities on the left sides are mutually equivalent. This generalizes a classical result of Hardy–Littlewood
Let σ be a weight function such that σ/1−z2α is in the class Bp0α of Békollé weights, μ a normal wei...
Let N denote the set of all positive integers and N0=N∪{0}. For m∈N, let Bm={z∈Cm:|z|1} be the open ...
We introduce an integral-type operator, denoted by Pφg, on the space of holomorphic functions on the...
AbstractFor 0<p,α<∞, let ‖f‖p,α be the Lp-norm with respect the weighted measure dVα(z)=δD(z)α−1dV(z...
ABSTRACT. It was shown in [2] that a holomorphic function f in the unit ball Bn of Cn belongs to the...
Let B denote the unit ball in Cⁿ, and ν the normalized Lebesgue measure on B. For α>-1, define dνα(z...
Let D be the open unit disk in the complex plane. For ε> 0 we consider the sector Σε = {z ∈ C: |...
<正> Let φ be a normal function on [0,1) and A'(φ)(1<P<∞) Bergman space on the unit ...
Given a finite set σ of the unit disc D = {z ∈ C:, |z | < 1} and a holomorphic function f in D wh...
AbstractLet D ⊂⊂Cn be a domain and D′ ⊂ D a closed complex submanifold. A normalized weight function...
ABSTRACT. We obtain several new characterizations for the standard weighted Bergman spaces Apα on th...
Let $A^p(\varphi)$ be the $p$-th Bergman space consisting of all holomorphic functions $f$ on t...
Given a finite set σ of the unit disc D = {z ∈ C:, |z | < 1} and a holomorphic function f in D wh...
Let Ω and ∏ be two simply connected proper subdomains of the complex plane ℂ. We are concerned with ...
International audienceGiven a finite set $\sigma$ of the unit disc $\mathbb{D}$ and a holomorphic fu...
Let σ be a weight function such that σ/1−z2α is in the class Bp0α of Békollé weights, μ a normal wei...
Let N denote the set of all positive integers and N0=N∪{0}. For m∈N, let Bm={z∈Cm:|z|1} be the open ...
We introduce an integral-type operator, denoted by Pφg, on the space of holomorphic functions on the...
AbstractFor 0<p,α<∞, let ‖f‖p,α be the Lp-norm with respect the weighted measure dVα(z)=δD(z)α−1dV(z...
ABSTRACT. It was shown in [2] that a holomorphic function f in the unit ball Bn of Cn belongs to the...
Let B denote the unit ball in Cⁿ, and ν the normalized Lebesgue measure on B. For α>-1, define dνα(z...
Let D be the open unit disk in the complex plane. For ε> 0 we consider the sector Σε = {z ∈ C: |...
<正> Let φ be a normal function on [0,1) and A'(φ)(1<P<∞) Bergman space on the unit ...
Given a finite set σ of the unit disc D = {z ∈ C:, |z | < 1} and a holomorphic function f in D wh...
AbstractLet D ⊂⊂Cn be a domain and D′ ⊂ D a closed complex submanifold. A normalized weight function...
ABSTRACT. We obtain several new characterizations for the standard weighted Bergman spaces Apα on th...
Let $A^p(\varphi)$ be the $p$-th Bergman space consisting of all holomorphic functions $f$ on t...
Given a finite set σ of the unit disc D = {z ∈ C:, |z | < 1} and a holomorphic function f in D wh...
Let Ω and ∏ be two simply connected proper subdomains of the complex plane ℂ. We are concerned with ...
International audienceGiven a finite set $\sigma$ of the unit disc $\mathbb{D}$ and a holomorphic fu...
Let σ be a weight function such that σ/1−z2α is in the class Bp0α of Békollé weights, μ a normal wei...
Let N denote the set of all positive integers and N0=N∪{0}. For m∈N, let Bm={z∈Cm:|z|1} be the open ...
We introduce an integral-type operator, denoted by Pφg, on the space of holomorphic functions on the...
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