Throughout, w, Γ, and∧ denote the classes of all, entire, and analytic scalar-valued single sequences, respectively. We write w2 for the set of all complex sequences (xmn), where m,n ∈ N is the set of positive integers. Then, w2 is a linear space under the coordinatewise addition and scalar multiplication. Some initial works on double sequence spaces are found in Bromwich [1]. Later on, they we...

We establish a generalized Jensen’s inequality for analytic vector-valued functions on TN using a monotonicity property of vector-valued Hardy martingales. We then discuss how this result extends to functions on a compact abelian group G, which are analytic with respect to an order on the dual group. We also give a generalization of Helson and Lowdenslager’s version of Jensen’s inequality to ce...

The adjoint of a composition operator on H2 induced by a rational function is computed explicitly as a multiple valued weighted composition operator. This computation is based on an expression for the adjoint of a composition operator on the Hardy space, and many other functional Hilbert spaces, as an integral operator. The formula for the adjoint of a composition operator on H2 with rational s...

In this paper we are concerned with hyponormality and subnormality of block Toeplitz operators acting on the vector-valued Hardy space H Cn of the unit circle. Firstly, we establish a tractable and explicit criterion on the hyponormality of block Toeplitz operators having bounded type symbols via the triangularization theorem for compressions of the shift operator. Secondly, we consider the gap...

We study subnormal Toeplitz operators on the vector-valued Hardy space of the unit circle, along with an appropriate reformulation of P.R. Halmos’s Problem 5: Which subnormal block Toeplitz operators are either normal or analytic ? We extend and prove Abrahamse’s Theorem to the case of matrix-valued symbols; that is, we show that every subnormal block Toeplitz operator with bounded type symbol ...

Let A be a general expansive matrix and let X ball quasi-Banach function space on $${\mathbb {R}}^n$$ , whose certain power (namely its convexification) supports Fefferman–Stein vector-valued maximal inequality the associate of other boundedness powered Hardy–Littlewood operator. The authors first introduce some anisotropic Campanato-type spaces associated with both X, prove that these are dual...