Let $T$ be a bounded operator on the Banach space $X$ and $ph$ be an analytic self-map of the unit disk $Bbb{D}$‎. ‎We investigate some operator theoretic properties of‎ ‎bilateral composition operator $C_{ph‎, ‎T}‎: ‎f ri T circ f circ ph$ on the vector-valued Hardy space $H^p(X)$ for $1 leq p leq‎ ‎+infty$.‎ ‎Compactness and weak compactness of $C_{ph‎, ‎T}$ on $H^p(X)$‎ ‎are characterized an...

In this paper, we establish a weighted version of the well-known Fréchet–Kolmogorov theorem, which holds for weights beyond \(A_\infty \). This theory extends previous known unsatisfactory results in terms relaxing index to natural range. As applications, obtain compactness commutators multilinear vector-valued Calderón–Zygmund type operators, including Littlewood–Paley operators. It is worthy ...

In previous work we established a multilinear duality and factorisation theory for norm inequalities pointwise weighted geometric means of positive linear operators defined on normed lattices. this paper extend the reach first time to setting general spaces. The scope includes Fourier restriction-type inequalities. We also sharpen our operators. Our results all share common theme: estimates mea...

In this paper, we will obtain the strong type and weak type estimates for vector-valued analogs of intrinsic square functions in the generalized weighted Morrey spacesM w (l2). We study the boundedness of intrinsic square functions including the Lusin area integral, the Littlewood-Paley g-function and gλ -function, and their multilinear commutators on vector-valued generalized weighted Morrey s...