A multiplier inclusion theorem on product domains

In this note it is shown that the class of all multipliers from the d-parameter Hardy space $H_{{\rm prod}}^1 ({\open T}^d)$ to L2 (𝕋d) is properly contained in the class of all multipliers from L logd/2L (𝕋d) to L2(𝕋d).

E-eigenvalue inclusion theorems for tensors

Two Z-eigenvalue inclusion theorems for tensors presented by Wang et al. (Discrete Cont. Dyn.-B, 2017, 22(1): 187-198) are first generalized to E-eigenvalue inclusion theorems. And then a tighter E-eigenvalue inclusion theorem for tensors is established. Based on the new set, a sharper upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained. Finally, numerical examples are given to verify the theoretical results.

On the inclusion of classes of functions, being integrable with a weight on the interval and satisfying conditions of Lipschitz type

We obtain generalization of Hardy and Littlewood inclusion theorem for some classes of functions being integrable with a weight on $[-1;1]$.

A Rogalski-Cornet Type Inclusion Theorem Based on Two Hausdorff Locally Convex Vector Spaces

A Rogalski-Cornet type inclusion theorem based on two Hausdorff locally convex vector spaces is proved and composed of two parts. An example is presented to show that the associated set-valued map in the first part does not need any conventional continuity conditions including upper hemicontinuous. As an application, solvability results regarding an abstract von Neumann inclusion system are obtained.

COMPARISON OF SPEEDS OF CONVERGENCE IN RIESZ‐TYPE FAMILIES OF SUMMABILITY METHODS. II

Certain summability methods for functions and sequences are compared by their speeds of convergence. The authors are extending their results published in paper [9] for Riesz‐type families {Aα} (α > α0 ) of summability methods Aα . Note that a typical Riesz‐type family is the family formed by Riesz methods Aα = (R, α), α > 0. In [9] the comparative estimates for speeds of convergence for two methods Aγ and Aβ in a Riesz‐type family {Aα}were proved on the base of an inclusion theorem. In the present paper these estimates are improved by comparing speeds of three methods Aγ, Aβ and Aδ on the base of a Tauberian theorem. As a result, a Tauberian remainder theorem is proved. Numerical examples given in [9] are extended to the present paper as applications of the Tauberian remainder theorem proved here.