scholarly journals Multiplicative Isometries on ClassesMp(X)of Holomorphic Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Yasuo Iida ◽  
Kazuhiro Kasuga
Keyword(s):  
Positive Integer ◽  
Holomorphic Functions ◽  
Smirnov Class ◽  
Linear Isometries

In (Iida and Kasuga 2013), the authors described multiplicative (but not necessarily linear) isometries ofMp(X)ontoMp(X)in the case of positive integerp∈N, whereMp(X)  (p≥1)is included in the Smirnov classN∗(X). In this paper, we will generalize the result to arbitrary (not necessarily positive integer) value of the exponents0<p<∞.

scholarly journals Multiplicative Isometries on SomeF-Algebras of Holomorphic Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Yasuo Iida ◽  
Kazuhiro Kasuga
Keyword(s):  
Holomorphic Functions ◽  
Smirnov Class ◽  
Algebras Of Holomorphic Functions ◽  
Linear Isometries

Multiplicative(but not necessarily linear) isometries ofMp(X)ontoMp(X)will be described, whereMp(X)(p≥1) areF-algebras included in the Smirnov classN∗(X).

scholarly journals A normal criterion concerning zero numbers

2021 ◽  
Author(s):  
Chengxiong Sun
Keyword(s):  
Positive Integer ◽  
Meromorphic Functions ◽  
Holomorphic Functions ◽  
Normal Criterion

AbstractLet $$n \ge 4$$ n ≥ 4 be a positive integer, $$\mathcal {F}$$ F be a family of meromorphic functions in D and let $$a(z)(\not \equiv 0), b(z)$$ a ( z ) ( ≢ 0 ) , b ( z ) be two holomorphic functions in D. If, for any function $$f \in \mathcal { F}$$ f ∈ F , (1)$$f(z) \ne \infty $$ f ( z ) ≠ ∞ when $$a(z)=0$$ a ( z ) = 0 , (2) $$f'(z)-a(z)f^{n}(z)-b(z)$$ f ′ ( z ) - a ( z ) f n ( z ) - b ( z ) has at most one zero in D, then $$\mathcal {F}$$ F is normal in D.

Exceptional functions and normal families of holomorphic functions with multiple zeros

2011 ◽  
Vol 18 (1) ◽  
pp. 31-38
Author(s):  
Jun-Fan Chen
Keyword(s):  
Positive Integer ◽  
Meromorphic Functions ◽  
Normal Family ◽  
Holomorphic Functions ◽  
Normal Families ◽  
Multiple Zeros ◽  
Zeros Of Functions

Abstract Let k be a positive integer, and let ℱ be a family of functions holomorphic on a domain D in C, all of whose zeros are of multiplicity at least k + 1. Let h be a function meromorphic on D, h ≢ 0, ∞. Suppose that for each ƒ ∈ ℱ, ƒ(k)(z) ≠ h(z) for z ∈ D. Then ℱ is a normal family on D. The condition that the zeros of functions in ℱ are of multiplicity at least k + 1 cannot be weakened, and the corresponding result for families of meromorphic functions is no longer true.

scholarly journals Weighted Differentiation Composition Operator from Logarithmic Bloch Spaces to Zygmund-Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Huiying Qu ◽  
Yongmin Liu ◽  
Shulei Cheng
Keyword(s):  
Positive Integer ◽  
Unit Disk ◽  
Composition Operator ◽  
Holomorphic Functions ◽  
Bloch Spaces ◽  
Type Spaces

LetH(𝔻)denote the space of all holomorphic functions on the unit disk𝔻ofℂ,u∈H(𝔻)and let  nbe a positive integer,φa holomorphic self-map of𝔻, andμa weight. In this paper, we investigate the boundedness and compactness of a weighted differentiation composition operator𝒟φ,unf(z)=u(z)f(n)(φ(z)),f∈H(𝔻), from the logarithmic Bloch spaces to the Zygmund-type spaces.

scholarly journals Multiplicative Isometries onF-Algebras of Holomorphic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Osamu Hatori ◽  
Yasuo Iida ◽  
Stevo Stević ◽  
Sei-Ichiro Ueki
Keyword(s):  
Unit Ball ◽  
Holomorphic Functions ◽  
Open Unit ◽  
Open Unit Ball ◽  
Smirnov Class ◽  
Unit Polydisk ◽  
Algebras Of Holomorphic Functions

We study multiplicative isometries on the followingF-algebras of holomorphic functions: Smirnov classN*(X), Privalov classNp(X), Bergman-Privalov classANαp(X),and ZygmundF-algebraNlogβN(X),whereXis the open unit ball&#x1D539;nor the open unit polydisk&#x1D53B;ninℂn.

Isometries of some F-algebras of holomorphic functions on the upper half plane

2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Yasuo Iida ◽  
Kei Takahashi
Keyword(s):  
Half Plane ◽  
Holomorphic Functions ◽  
Upper Half Plane ◽  
Algebras Of Holomorphic Functions ◽  
Linear Isometries

AbstractLinear isometries of N p(D) onto N p(D) are described, where N p(D), p > 1, is the set of all holomorphic functions f on the upper half plane D = {z ∈ ℂ: Im z > 0} such that supy>0 ∫ℝ lnp (1 + |(x + iy)|) dx < +∞. Our result is an improvement of the results by D.A. Efimov.

Isometries of Weighted Bergman Spaces

1982 ◽  
Vol 34 (4) ◽  
pp. 910-915 ◽  
Author(s):  
Clinton J. Kolaski
Keyword(s):  
Bergman Space ◽  
Bergman Spaces ◽  
Holomorphic Functions ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Bounded Symmetric Domains ◽  
General Argument ◽  
Image Position ◽  
Linear Isometries

In [2], [8] and [10], Forelli, Rudin and Schneider described the isometries of the Hp spaces over balls and polydiscs. Koranyi and Vagi [6] noted that their methods could be used to describe the isometries of the Hp spaces over bounded symmetric domains. Recently Kolaski [4] observed that the algebraic techniques used above and Rudin's theorem on equimeasurability extended to the Bergman spaces over bounded Runge domains. In this paper we use the same general argument to characterize the onto linear isometries of the weighted Bergman spaces over balls and polydiscs, (all isometries referred to are assumed to be linear).2. Preliminaries. Horowitz [3] first defined the weighted Bergman space Ap,α(0 < p < ∞, 0 < α < ∞) to be the space of holomorphic functions f in the disc which satisfy(1)

scholarly journals Normality Criteria of Meromorphic Functions That Share a Holomorphic Function

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Jie Ding ◽  
Jianming Qi ◽  
Taiying Zhu
Keyword(s):  
Positive Integer ◽  
Holomorphic Function ◽  
Meromorphic Functions ◽  
Holomorphic Functions

LetFbe a family of meromorphic functions defined inD, letψ(≢0),a0,a1,...,ak-1be holomorphic functions inD, and letkbe a positive integer. Suppose that, for every functionf∈F,f≠0,P(f)=f(k)+ak-1f(k-1)+⋯+a1f'+a0f≠0and, for every pair functions(f,g)∈F,P(f),P(g)shareψ, thenFis normal inD.

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