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 uCφ from Zygmund type spaces to Bloch type spaces in D in terms of u, φ, their derivatives, and φn, the n-th power of φ. Moreover, we obtain some similar estimates for the essential norms of the operators uCφ, from which sufficient and necessary conditions of compactness of uCφ follows immediately., Xin-Cui Guo, Ze-Hua Zhou., and Obsahuje seznam literatury
Tapeworms of the order Spathebothriidea Wardle et McLeod, 1952 (Cestoda) are reviewed. Molecular data made it possible to assess, for the first time, the phylogenetic relationships of all genera and to confirm the validity of Bothrimonus Duvernoy, 1842, Diplocotyle Krabbe, 1874 and Didymobothrium Nybelin, 1922. A survey of all species considered to be valid is provided together with new data on egg and scolex morphology and surface ultrastructure (i.e. microtriches). The peculiar morphology of the members of this group, which is today represented by five effectively monotypic genera whose host associations and geographical distribution show little commonality, indicate that it is a relictual group that was once diverse and widespread. The order potentially represents the earliest branch of true tapeworms (i.e. Eucestoda) among extant forms.