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We establish the test which allows to show that a mean does not admit a weak-Hardy property. As a result we prove that Hardy and weak-Hardy properties are equivalent in the class of homogeneous, symmetric, repetition invariant, and Jensen concave mean on $\mathbb{R}_+$. More precisely, for every mean $\mathscr{M} \colon \bigcup_{n=1}^\infty \mathbb{R}_+^n \to \mathbb{R}$ as above, the inequality $$\mathscr{M}(a_1)+\mathscr{M}(a_1,a_2)+\dots

In the present paper we are going to prove some necessary condition for a mean to be Hardy. This condition is then applied to completely characterize the Hardy property among the Gini means., 6 pages

Each family $\mathcal{M}$ of means has a natural, partial order (point-wise order), that is $M \le N$ iff $M(x) \le N(x)$ for all admissible $x$. In this setting we can introduce the notion of interval-type set (a subset $\mathcal{I} \subset \mathcal{M}$ such that whenever $M \le P \le N$ for some $M,\,N \in \mathcal{I}$ and $P \in \mathcal{M}$ then $P \in \mathcal{I}$). For example, in the case of power means there exists a natural isomorphism between interval-type sets and intervals contained in real numbers. Nevertheless there appear a number of interesting objects for a families which cannot be linearly ordered. In the present paper we consider this property for Gini means and Hardy means. Moreover some results concerning $L^\infty$ metric among (abstract) means will be obtained., Comment: 8 pages

The purpose of this paper is to prove some facts about integral means of (d2/dz2)(log[f(z)/z])—or equivalently f″/f, for f in a class of starlike mappings of a "singular" nature. In particular it is noted that the Koebe function is not extremal for the Hardy means Mp(r,f″/f) for functions in this class.

Preface. - Applications of Blaschke products to the spectral theory of Toeplitz operators (Grudsky, Shargorodsky). -A survey on Blaschke-oscillatory differential equations, with updates (Heittokangas.). - Bi-orthogonal expansions in the space L2(0,1) ( Boivin, Zhu). - Blaschke products as solutions of a functional equation (Mashreghi.). - Cauchy Transforms and Univalent Functions( Cima, Pfaltzgraff). - Critical points, the Gauss curvature equation and Blaschke products (Kraus, Roth). - Growth, zero distribution and factorization of analytic functions of moderate growth in the unit disc, (Chyzhykov, Skaskiv). - Hardy means of a finite Blaschke product and its derivative ( Gluchoff, Hartmann). -Hyperbolic derivatives determine a function uniquely (Baribeau). - Hyperbolic wavelets and multiresolution in the Hardy space of the upper half plane (Feichtinger, Pap). - Norm of composition operators induced by finite Blaschke products on Mobius invariant spaces (Martin, Vukotic). - On the computable theory of bounded analytic functions (McNicholl). - Polynomials versus finite Blaschke products ( Tuen Wai Ng, Yin Tsang). -Recent progress on truncated Toeplitz operators (Garcia, Ross).