Showing papers by "Stevo Stević published in 2010"
TL;DR: The boundedness and compactness of weighted differentiation composition operators from the space of bounded analytic functions, the Bloch space and the little Blochspace to nth weighted-type spaces on the unit disk are characterized.
110 citations
TL;DR: In this article, the boundedness and compactness of the integral-type operator I φ g ( f ) ( z ) = ∫ 0 1 R f ( φ ( t z ) ) g ( t t, z ∈ B, where g is a holomorphic function on the unit ball B ⊂ C n such that g ( 0 ) = 0, and φ is a self-map of B, acting from α -Bloch spaces to Bloch-type spaces on B.
Abstract: We characterize the boundedness and compactness of the following integral-type operator I φ g ( f ) ( z ) = ∫ 0 1 R f ( φ ( t z ) ) g ( t z ) d t t , z ∈ B , where g is a holomorphic function on the unit ball B ⊂ C n such that g ( 0 ) = 0 , and φ is a holomorphic self-map of B , acting from α -Bloch spaces to Bloch-type spaces on B .
81 citations
TL;DR: It is shown that every positive solution to the difference equation x"n=maxA"1x"n"-"p" shows that 1,2,3,4 are natural numbers such that 1=0,@a"i@?(-1,1),i=1,...,k, converges to max"1" =<"i"=<"kA"i^1^@a^"^i^+^1.
70 citations
TL;DR: In this article, the boundedness character of positive solutions of the following generalization of a max-type difference equation from automatic control theory was studied, where the parameters A, p, q and r are positive numbers.
Abstract: This paper studies the boundedness character of positive solutions of the following generalization of a max-type difference equation from automatic control theory (see, Mishkis, (1977) [18] and Popov (1966) [21] ) x n + 1 = max { A , x n p x n − 1 q x n − 2 r } , n ∈ N 0 , where the parameters A , p , q and r are positive numbers. In the study of the equation we also introduce a new method called Oachkatzlschwoif.
69 citations
TL;DR: The boundedness and compactness of the products of differentiation and composition operators from Zygmund spaces to Bloch spaces and Bers spaces are discussed.
68 citations
TL;DR: The boundedness and compactness of the product of the differentiation and composition operator from the space of bounded analytic functions, the Bloch space and the little Blochspace to nth weighted-type spaces on the unit disk are characterized.
62 citations
TL;DR: The boundedness and compactness of the following recently introduced integral-type operatorP, "@f^gf(z)[email protected]!"0^1f(@f(tz))g(tz)dtt,[email protected]?B, are studied.
47 citations
TL;DR: The first lemma can be proved in a standard way see, e.g., in 13, Proposition 3.11 or in 15, Lemma 3. Lemma 2.1.
Abstract: and Applied Analysis 3 2. Auxiliary Results Here we quote some auxiliary results which will be used in the proofs of the main results. The first lemma can be proved in a standard way see, e.g., in 13, Proposition 3.11 or in 15, Lemma 3 . Lemma 2.1. Assume that m ∈ N0, n ∈ N, p, q > 0, γ > −1, φ is an analytic self-map of D and u ∈ H D . Then the operator D φ,u : Hp,q,γ → W n μ is compact if and only if D φ,u : Hp,q,γ → W n μ is bounded and for any bounded sequence fk k∈N in Hp,q,γ which converges to zero uniformly on compact subsets of D, D φ,ufk → 0 inW n μ as k → ∞. The next lemma is known, but we give a proof of it for the benefit of the reader. Lemma 2.2. Assume that n ∈ N0, 0 −1 and m > 1 β one has ∫1 0 1 − r β ( 1 − ρrm ≤ C ( 1 − ρ) β−m, 0 0 and Dn a ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ 1 1 · · · 1 a a 1 · · · a n − 1 a a 1 a 1 a 2 · · · a n − 1 a n · · · n−2 ∏
40 citations
TL;DR: The boundedness and compactness of the following integral-type operator L"gf(z)[email protected]!"0^1Rf(tz)g (tz)dtt,[email-protected]?B is characterized.
40 citations
TL;DR: The boundedness and compactness of an integral-type operator from Zygmund-type spaces to the mixed norm space on the unit ball were characterized in this paper, where the integral type operator was shown to be compact.
Abstract: The boundedness and compactness of an integral-type operator recently introduced by the author from Zygmund-type spaces to the mixed-norm space on the unit ball are characterized here.
39 citations
TL;DR: In this paper, the integral operator norm and essential norm of an integral type operator from the Dirichlet space to the Bloch-type space on the unit ball in ℂ𝑛 are calculated.
Abstract: Operator norm and essential norm of an integral-type operator, recently introduced by this author, from the Dirichlet space to the Bloch-type space on the unit ball in ℂ𝑛 are calculated here.
TL;DR: The boundedness and compactness of weighted iterated radial composition operators from the mixed-norm space to the weighted type space and the little weighted-type space on the unit ball are characterized in this paper.
Abstract: The boundedness and compactness of weighted iterated radial composition operators from the mixed-norm space to the weighted-type space and the little weighted-type space on the unit ball are characterized here. We also calculate the Hilbert-Schmidt norm of the operator on the weighted Bergman-Hilbert space as well as on the Hardy 𝐻2 space.
TL;DR: The boundedness of the composition operator C"@ff(z)=f(@ f(@f(z)") from the Hardy space H^p(X),p>0, where X is the upper half-plane of the complex plane C, is characterized.
TL;DR: In this article, the authors investigated the boundedness and compactness of the weighted composition between -Bloch space (little-bloch space) and -bloch spaces on the unit polydisc of and a holomorphic self-map of.
Abstract: For , let denote the -Bloch space on the unit polydisc of and a holomorphic self-map of . We investigate the boundedness and compactness of the weighted composition between -Bloch space (little -Bloch space ) and -Bloch space (little -Bloch space ). The most important result in the paper is that conditions for the compactness are different for the cases and , unlike for the case of the weighted operators on the unit disc. Bibliography: 32 titles.
TL;DR: The boundedness and compactness of weighted composition operators from the Bergman–Privalov-type space to weighted-type and the little weighted- type space on the unit ball in C n is characterized.
TL;DR: The boundedness and compactness of an integral-type operator, which has been recently introduced by the first author, between weighted-type spaces and Bloch- type spaces on the unit ball are studied here.
TL;DR: It is shown that every positive solution to the difference equation yn converges to one and this result confirms a quite recent conjecture posed by Liu and Yang (2010) in [10].
TL;DR: Operator norm of the multiplication operator on the weighted Bergman space A"@a^p(D), as well as of weighted composition operator from A" @a^ p(D) to a weighted-type space are calculated.
TL;DR: The weighted composition operator is investigated from the weighted Bergman space into the weighted Hardy space on the unit ball and a characterization for the boundedness and compactness of the operator whose the target space is the Hardy space is given.
TL;DR: An asymptotically equivalent expression to the essential norm of differences of weighted composition operators between weighted-type spaces of holomorphic functions on the unit ball in C N is found.
TL;DR: The boundedness and compactness of the following integral-type operator G(f)(z) is studied, which describes the space of holomorphic functions on the unit ball B@?C^n.
TL;DR: In this article, the authors studied the boundedness and compactness of the integral-type operator between Bloch-type spaces and, where is a normal weight function and is a weight function.
Abstract: Let denote the open unit ball of . For a holomorphic self-map of and a holomorphic function in with , we define the following integral-type operator: , . Here denotes the radial derivative of a holomorphic function in . We study the boundedness and compactness of the operator between Bloch-type spaces and , where is a normal weight function and is a weight function. Also we consider the operator between the little Bloch-type spaces and .
TL;DR: Operator norm is calculated of the multiplication operator on the Hardy space H p ( D ) as well as of the weighted composition operator from Hp ( D) to a weighted-type space.
Journal Article•
TL;DR: The compactness of differences of weighted composition operators from the weighted Bergman space A α p to the weighted-type space H v ∞ of analytic functions on the open unit disk D is characterized in terms of inducing symbols φ 1, φ 2: D → D and u 1, u 2 : D → C.
TL;DR: In this paper, the main results in the work of Yalcinkaya et al. are given very short and elegant proofs of the main result in their paper. But they do not give any proofs of their work in this paper.
Abstract: We give very short and elegant proofs of the main results in the work of Yalcinkaya et al. (2008).
TL;DR: In this article, a useful max-type difference inequality which can be applied in studying of some max type difference equations and give an application of it in a recent problem from the research area is presented.
Abstract: We prove a useful max-type difference inequality which can be applied in studying of some max-type difference equations and give an application of it in a recent problem from the research area. We also give a representation of solutions of the difference equation 𝑥𝑛=max{𝑥𝑎1𝑛−1,…,𝑥𝑎𝑘𝑛−𝑘}.
TL;DR: The boundedness and compactness of the weighted composition operator uC"@f is characterized, which is a holomorphic self-map of a bounded, circular, strictly convex domain in C^n with C^2 boundary.