Multipliers of Lorentz spaces

Multipliers of generalized frames in Hilbert spaces

Multipliers of Spaces of Derivatives

For subspaces, X and Y , of the space, D, of all derivatives M(X, Y ) denotes the set of all g ∈ D such that fg ∈ Y for all f ∈ X. Subspaces of D are defined depending on a parameter p ∈ [0,∞]. In Section 6, M(X, D) is determined for each of these subspaces and in Section 7, M(X, Y ) is found for X and Y any of these subspaces. In Section 3, M(X, D) is determined for other spaces of functions o...

Calderón couples of Lorentz spaces

We present some sufficient conditions under which pairs of Banach function lattices are Calderón couples with special attention to the case of classical Lorentz spaces.

Comparison of Orlicz–Lorentz Spaces

Orlicz–Lorentz spaces provide a common generalization of Orlicz spaces and Lorentz spaces. They have been studied by many authors, including Masty lo, Maligranda, and Kamińska. In this paper, we consider the problem of comparing the Orlicz–Lorentz norms, and establish necessary and sufficient conditions for them to be equivalent. As a corollary, we give necessary and sufficient conditions for a...

Are Generalized Lorentz “spaces” Really Spaces?

We show that the Lorentz space Λp(w) need not be a linear set for certain “non-classical” weights w. We establish necessary and sufficient conditions on p and w for this situation to occur.