Showing papers by "Stevo Stević published in 2009"
TL;DR: In this article, an integral-type operator on the space H (B ) of all holomorphic functions on the unit ball B ⊂ C n P φ g ( f ) ( z ) = ∫ 0 1 f ( φ ( t z ) ) g ( t t, z ∈ B, where g ∈ H ( B ), g ( 0 ) = 0 and φ is a holomorphic self-map of B.
126 citations
TL;DR: In this article, an integral operator on the unit ball is introduced and boundedness and compactness of the operator from the Zygmund space to the Bloch-type space or the little Bloch type space are investigated.
Abstract: In this paper, we introduce an integral operator on the unit ball . The boundedness and compactness of the operator from the Zygmund space to the Bloch-type space or the little Bloch-type space are investigated.
98 citations
TL;DR: All the solutions of a rational difference equation from Putnam's mathematical competition are described, which are eventually equal to its positive equilibrium, and a new, elegant and short proof of the fact that the equation has a positive solution which is not eventuallyequal to one.
89 citations
TL;DR: In this article, the Hilbert-Schmidt norms of products of composition and differentiation operators on the Bergman space and Hardy space were derived in terms of the generalized Nevanlinna counting function.
Abstract: Motivated by a recent paper by S. Ohno we calculate Hilbert-Schmidt norms of products of composition and differentiation operators on the Bergman space $A^2_\alpha,$ $\alpha>-1$ and the Hardy space $H^2$ on the unit disk. When the convergence of sequences $(\varphi_n)$ of symbols to a given symbol $\varphi$ implies the convergence of product operators $C_{\varphi_n}D^k$ is also studied. Finally, the boundedness and compactness of the operator $C_{\varphi}D^k: A^2_\alpha\to A^2_\alpha$ are characterized in terms of the generalized Nevanlinna counting function.
88 citations
TL;DR: The norm of composition followed by differentiation operator from the Bloch and the little Bloch space to the weighted space H μ ∞ on the unit disk is calculated.
88 citations
TL;DR: A complete picture on the boundedness and compactness of integral-type operators and composition operators between Bloch-type spaces of holomorphic functions on the unit disk is given in this article.
87 citations
TL;DR: The boundedness and compactness of the weighted differentiation composition operator D"@f","u^n(f)(z)=u(z)f^(^n^)(@f(z), where u is a holomorphic function on the unit disk D, @f is a Holomorphic self-map of D and [email protected]?N"0 is studied.
77 citations
TL;DR: In particular, for the case p k − 1 ∈ ( 0, k k / (k − 1 ) k−1 ) k −1 ) as mentioned in this paper, it was shown that all solutions to the difference equation are bounded.
Abstract: A complete picture regarding the boundedness character of positive solutions to the following difference equation x n = max { A , x n − 1 p x n − k p } , n ∈ N 0 , where k ≥ 2 and the parameters A and p are positive real numbers, is given. In particular, for the case p k − 1 ∈ ( 0 , k k / ( k − 1 ) k − 1 ) , we prove that all solutions to the equation are bounded. We also present corresponding results concerning the following closely related difference equation x n = A + x n − 1 p x n − k p , n ∈ N 0 .
76 citations
TL;DR: In this paper, the authors introduce a new space of analytic functions on the unit ball, the so-called iterated logarithmic Bloch space B log k, and study some of its properties.
Abstract: We introduce a new space of analytic functions on the unit ball, the so-called iterated logarithmic Bloch space B log k , and study some of its properties. Among other features, we study the boundedness and compactness of weighted composition operators on the unit disk, as well as of a recently introduced integral-type operator on the unit ball, with (i) domain the iterated logarithmic Bloch space B log k , or the little iterated logarithmic Bloch space B log k , 0 and (ii) range the Bloch-type space B μ , or the little-Bloch-type space B μ , 0 , or the weighted space H μ ∞ , or the little weighted space H μ , 0 ∞ .
75 citations
TL;DR: It is proved that every positive solution to the difference equation x"n=maxA"1x"n"-"1^@a^"^1, A"2x" n"-"2^@ a^" ^2,...,A"kx"N"-"k#@a#"^k", and another result on global convergence which concerns some cases when not all @a,i=1,...,k belong to the interval (0,1).
71 citations
TL;DR: In this paper, the boundedness and compactness of the integral-type operator P φ g f (z ) = ∫ 0 1 f ( φ ( t z ) ) g (t z ) d t t, z ∈ B, where φ is a holomorphic self-map of the unit ball B in C n and g is a function on B such that g ( 0 ) = 0, from logarithmic Bloch-type and mixed-norm spaces to Bloch type spaces.
Abstract: This paper studies the boundedness and compactness of the following integral-type operator, recently introduced by this author, P φ g f ( z ) = ∫ 0 1 f ( φ ( t z ) ) g ( t z ) d t t , z ∈ B , where φ is a holomorphic self-map of the unit ball B in C n and g is a holomorphic function on B such that g ( 0 ) = 0 , from logarithmic Bloch-type and mixed-norm spaces to Bloch-type spaces.
Journal Article•
TL;DR: In this paper, the authors give a complete picture of the boundedness and compactness of the products of integral-type operators and composition operators from the mixed norm space to Bloch-type spaces of holomorphic functions on the unit disk.
Abstract: We give a complete picture of the boundedness and compactness of the products of integral-type operators and composition operators from the mixed norm space to Bloch-type spaces of holomorphic functions on the unit disk.
TL;DR: The boundedness and compactness of the following integral-type operators are studied, between weighted-type spaces on the unit ball.
TL;DR: The operator norm of the weighted composition operator is calculated from a weighted Bergman space to a weighted-type space on the unit ball of C^n and the compactness of the operator is characterized.
TL;DR: The operator T g can be considered as an extension of the Cesaro operator on the unit disk and the boundedness and compactness of the operators T g and L g, on the Zygmund space and from the Ziegmund space to the Bloch space are studied.
TL;DR: This work calculates in an elegant way operator norm of the weighted composition operator from the @a-Bloch space, with @a@?(0,~)@?{1}, to a weighted-type space on the unit ball.
TL;DR: In this paper, it was shown that every well-defined solution of the difference equation x n + 1 = max { A x n, x n − 2 }, n ∈ N 0, where A ∈ R is eventually periodic with period three.
Abstract: We show that every well-defined solution of the difference equation x n + 1 = max { A x n , x n − 2 } , n ∈ N 0 , where A ∈ R is eventually periodic with period three.
TL;DR: In this article, the boundedness and compactness of the integral-type operator from the mixed norm space H(p, q, ϕ) to the Bloch-type space ℬµ( \mathbb{B} \)).
Abstract: Let \( \mathbb{B} \) be the unit ball in ℂn and let H(\( \mathbb{B} \)) be the space of all holomorphic functions on \( \mathbb{B} \). We introduce the following integral-type operator on H(\( \mathbb{B} \)):
$$ I_\phi ^g (f)(z) = \int\limits_0^1 {\operatorname{Re} f(\phi (tz))g(tz)\frac{{dt}} {t}} ,z \in \mathbb{B}, $$
where g e H(\( \mathbb{B} \)), g(0) = 0, and φ is a holomorphic self-map of \( \mathbb{B} \). Under study are the boundedness and compactness of the operator from the mixed norm space H(p, q, ϕ)(\( \mathbb{B} \)) to the Bloch-type space ℬµ(\( \mathbb{B} \)).
TL;DR: The boundedness and compactness of the operator T"g from Bloch- type spaces to Zygmund-type spaces are studied.
TL;DR: A necessary and a sufficient condition for a function with Hadamard gaps to belong to the logarithmic Bloch-type space are given, as well as some applications of these results to a composition operator.
TL;DR: The extended Cesaro operators extended to the Hardy space of holomorphic functions on the unit ball B extend and simplify some one-dimensional results.
TL;DR: The boundedness and compactness of the weighted composition operators acting between some Fock-type spaces in C^N are characterized and some estimates for the essential norm of some of these operators are given.
TL;DR: This paper studies the boundedness character of the positive solutions of the difference equation x"n"+"1=A+x"n^px" n"-"1^qx"N"-"2^r,n@?N"0, where the parameters A,p,q and r are positive numbers.
TL;DR: In this paper, a comprehensive study of the boundedness, global asymptotic stability and periodic character for positive solutions of a higher-order difference equation of interest is presented.
Abstract: This paper presents a comprehensive study of the boundedness, global asymptotic stability and periodic character for positive solutions of a higher-order difference equation of interest.
TL;DR: The boundedness of the composition operator from the weighted Bergman space to the recently introduced by the author, the ǫth weighted space on the unit disc, is characterized in this article.
Abstract: The boundedness of the composition operator from the weighted Bergman space to the recently introduced by the author, the 𝑛th weighted space on the unit disc, is characterized. Moreover, the norm of the operator in terms of the inducing function and weights is estimated.
TL;DR: This paper studies the boundedness and compactness of the following integral-type operator, recently introduced by Xiangling Zhu and the second authorI"@f^gf(z)[email protected]!"0^1Rf(@f(tz))g(tz)dtt,[email protected]?B, from the iterated logarithmic Bloch spaces into the Bloch-type spaces.
Journal Article•
TL;DR: The Zygmund-type space was introduced in this article for the case ǫ = 2, and the main result of this paper is that the boundedness of the composition operator is bounded.
Abstract: Here we introduce the 𝑛 th
weighted space on the upper half-plane Π + = { 𝑧 ∈ ℂ ∶ I m 𝑧 > 0 } in the complex plane ℂ . For the case 𝑛 = 2 , we
call it the Zygmund-type space, and denote it by 𝒵 ( Π + ) . The main result of the
paper gives some necessary and sufficient conditions for the boundedness of
the composition operator 𝐶 𝜑 𝑓 ( 𝑧 ) = 𝑓 ( 𝜑 ( 𝑧 ) ) from the Hardy space 𝐻 𝑝 ( Π + ) on the upper half-plane, to the Zygmund-type space, where 𝜑 is an analytic
self-map of the upper half-plane.
TL;DR: This work calculates operator norms of the multiplication operators M"u(f)=uf, on the weighted Bergman space A"@a^p(X), as well as on the Hardy space H^p (X), where X is the unit polydisk D^n or the unit ball B in C^n.