Linear operators on for dispersed
We study linear operators from a non-locally convex Orlicz space to a Banach space . Recall that a linear operator is said to be σ-smooth whenever in implies . It is shown that every σ-smooth operator factors through the inclusion map , where Φ̅ denotes the convex minorant of Φ. We obtain the Bochner integral representation of σ-smooth operators . This extends some earlier results of J. J. Uhl concerning the Bochner integral representation of linear operators defined on a locally convex...
This paper is devoted to several questions concerning linearizations of function spaces. We first consider the relation between linearizations of a given space when it is viewed as a function space over different domains. Then we study the problem of characterizing when a Banach function space admits a Banach linearization in a natural way. Finally, we consider the relevance of compactness properties in linearizations, more precisely, the relation between different compactness properties of a mapping,...
We show the existence of Lipschitz approximable separable spaces which fail Grothendieck's approximation property. This follows from the observation that any separable space with the metric compact approximation property is Lipschitz approximable. Some related results are spelled out.
We study continuity envelopes of function spaces and where the weight belongs to the Muckenhoupt class ₁. This essentially extends partial forerunners in [13, 14]. We also indicate some applications of these results.
In the setting of a metric measure space (X, d, μ) with an n-dimensional Radon measure μ, we give a necessary and sufficient condition for the boundedness of Calderón-Zygmund operators associated to the measure μ on Lipschitz spaces on the support of μ. Also, for the Euclidean space Rd with an arbitrary Radon measure μ, we give several characterizations of Lipschitz spaces on the support of μ, Lip(α,μ), in terms of mean oscillations involving μ. This allows us to view the "regular" BMO space of...