A formula for the Bloch norm of a $C^1$-function on the unit ball of $\mathbb {C}^n$

Miroslav Pavlović

Displaying similar documents to “A formula for the Bloch norm of a $C^{1}$ -function on the unit ball of $ℂ^{n}$ ”

Distributivity of strong implications over conjunctive and disjunctive uninorms

Daniel Ruiz-Aguilera, Joan Torrens (2006)

Kybernetika

Similarity:

This paper deals with implications defined from disjunctive uninorms $U$ by the expression $I (x, y) = U (N (x), y)$ where $N$ is a strong negation. The main goal is to solve the functional equation derived from the distributivity condition of these implications over conjunctive and disjunctive uninorms. Special cases are considered when the conjunctive and disjunctive uninorm are a $t$ -norm or a $t$ -conorm respectively. The obtained results show a lot of new solutions generalyzing those obtained in previous works...

On the structure of continuous uninorms

Paweł Drygaś (2007)

Kybernetika

Similarity:

Uninorms were introduced by Yager and Rybalov [13] as a generalization of triangular norms and conorms. We ask about properties of increasing, associative, continuous binary operation $U$ in the unit interval with the neutral element $e \in [0, 1]$ . If operation $U$ is continuous, then $e = 0$ or $e = 1$ . So, we consider operations which are continuous in the open unit square. As a result every associative, increasing binary operation with the neutral element $e \in (0, 1)$ , which is continuous in the open unit square may be...

Optimality conditions for maximizers of the information divergence from an exponential family

František Matúš (2007)

Kybernetika

Similarity:

The information divergence of a probability measure $P$ from an exponential family $ℰ$ over a finite set is defined as infimum of the divergences of $P$ from $Q$ subject to $Q \in ℰ$ . All directional derivatives of the divergence from $ℰ$ are explicitly found. To this end, behaviour of the conjugate of a log-Laplace transform on the boundary of its domain is analysed. The first order conditions for $P$ to be a maximizer of the divergence from $ℰ$ are presented, including new ones when $P$ is not projectable...

On Ozeki’s inequality for power sums

Horst Alzer (2000)

Czechoslovak Mathematical Journal

Similarity:

Let $p \in (0, 1)$ be a real number and let $n \geq 2$ be an even integer. We determine the largest value $c_{n} (p)$ such that the inequality $\sum_{i = 1}^{n} {| a_{i} |}^{p} \geq c_{n} (p)$ holds for all real numbers $a_{1}, ..., a_{n}$ which are pairwise distinct and satisfy ${min}_{i \neq j} | a_{i} - a_{j} | = 1$ . Our theorem completes results of Ozeki, Mitrinović-Kalajdžić, and Russell, who found the optimal value $c_{n} (p)$ in the case $p > 0$ and $n$ odd, and in the case $p \geq 1$ and $n$ even.

New characterizations for weighted composition operator from Zygmund type spaces to Bloch type spaces

Xin-Cui Guo, Ze-Hua Zhou (2015)

Czechoslovak Mathematical Journal

Similarity:

Let $u$ be a holomorphic function and $ϕ$ a holomorphic self-map of the open unit disk $𝔻$ in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators $u C_{ϕ}$ from Zygmund type spaces to Bloch type spaces in $𝔻$ in terms of $u$ , $ϕ$ , their derivatives, and $ϕ^{n}$ , the $n$ -th power of $ϕ$ . Moreover, we obtain some similar estimates for the essential norms of the operators $u C_{ϕ}$ , from which sufficient and necessary conditions of compactness of $u C_{ϕ}$ follows immediately. ...

Displaying similar documents to “A formula for the Bloch norm of a C 1 -function on the unit ball of ℂ n ”

Distributivity of strong implications over conjunctive and disjunctive uninorms

On the structure of continuous uninorms

Optimality conditions for maximizers of the information divergence from an exponential family

On Ozeki’s inequality for power sums

New characterizations for weighted composition operator from Zygmund type spaces to Bloch type spaces

Displaying similar documents to “A formula for the Bloch norm of a $C^{1}$ -function on the unit ball of $ℂ^{n}$ ”