Localization principle for Triebel-Lizorkin spaces on spaces of homogeneous type.
The author establishes the localization principle for the Triebel-Lizorkin spaces on spaces of homogeneous type.
The author establishes the localization principle for the Triebel-Lizorkin spaces on spaces of homogeneous type.
Let X be a compact Hausdorff space and M a metric space. is the set of f ∈ C(X,M) such that there is a dense set of points x ∈ X with f constant on some neighborhood of x. We describe some general classes of X for which is all of C(X,M). These include βℕ, any nowhere separable LOTS, and any X such that forcing with the open subsets of X does not add reals. In the case where M is a Banach space, we discuss the properties of as a normed linear space. We also build three first countable Eberlein...
Let be a completely regular Hausdorff space and a real normed space. We examine the general properties of locally solid topologies on the space of all -valued continuous and bounded functions from into . The mutual relationship between locally solid topologies on and
Locally solid topologies on vector valued function spaces are studied. The relationship between the solid and topological structures of such spaces is examined.
The classical notion of Łojasiewicz ideals of smooth functions is studied in the context of non-quasianalytic Denjoy-Carleman classes. In the case of principal ideals, we obtain a characterization of Łojasiewicz ideals in terms of properties of a generator. This characterization involves a certain type of estimates that differ from the usual Łojasiewicz inequality. We then show that basic properties of Łojasiewicz ideals in the case have a Denjoy-Carleman counterpart.
Characterizations are obtained for those pairs of weight functions u and v for which the operators with a and b certain non-negative functions are bounded from to , 0 < p,q < ∞, p≥ 1. Sufficient conditions are given for T to be bounded on the cones of monotone functions. The results are applied to give a weighted inequality comparing differences and derivatives as well as a weight characterization for the Steklov operator.