We consider the mixed norm spaces of Hardy type studied by Flett and others. We study some properties of these spaces related to mean and pointwise growth and complement some partial results by various authors by giving a complete characterization of the inclusion between H (p, q, α) and H(u, v, β), depending on the parameters p, q, α, u, v and β.

We characterize the semigroups of composition operators that are strongly continuous on the mixed norm spaces H(p, q, α). First, we study the separable spaces H(p, q, α) with q < ∞, that behave as the Hardy and Bergman spaces. In the second part we deal with the spaces H(p, ∞, α), where polynomials are not dense. To undertake this study, we introduce the integral operators, characterize its boundedness and compactness, and use its properties to find the maximal closed linear subspace of H(p, ∞, α) in which the semigroups are strongly continuous. In particular, we obtain that this maximal space is either H(p, 0, α) or non-separable, being this result the deepest one in the paper.

We work with very general Banach spaces of analytic functions in the disk or other domains which satisfy a minimum number of natural axioms. Among the preliminary results, we discuss some implications of the basic axioms and identify all functional Banach spaces in which every bounded analytic function is a pointwise multiplier. Next, we characterize (in various ways) the weighted composition operators among the bounded operators on such spaces, thus generalizing some well-known results on multiplication or composition operators. We also characterize the invertible weighted composition operators on the disk and on general Banach spaces of analytic functions on bounded domains under different sets of axioms whose connections we discuss by providing appropriate examples. This generalizes and complements various recent results by Gunatillake, Bourdon, and Hyvärinen-Lindström-Nieminen-Saukko.

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Distributed Artificial Intelligence is attracting interest day by day. In this paper, the authors introduce an innovative methodology for distributed learning of Particle Swarm Optimization-based Fuzzy Cognitive Maps in a privacy-preserving way. The authors design a training scheme for collaborative FCM learning that offers data privacy compliant with the current regulation. This method is applied to a cancer detection problem, proving that the performance of the model is improved by the Federated Learning process, and obtaining similar results to the ones that can be found in the literature.