Analysis Mathematica最新文献

Let ({cal L} = - Delta + V) be a Schrödinger operator with a nonnegative potential V belonging to the reverse Hölder class B_q for q> n/2. In this paper, we study the weighted compactness of oscillation and variation commutators generated by BMO-type functions and some Schrödinger operators, which include Riesz transform and other standard Calderón–Zygmund operators.

This article describes the surjective linear isometries between spaces of p-times differentiable maps from a domain of the Euclidean space into a certain Banach space.

In this paper, we mainly show that if a product AB (or BA) of a closed symmetric operator A and a bounded positive operator B is normal, then it is self-adjoint. Equivalently, this means that B commutes with A. Certain generalizations and consequences are also presented.

Let G be a locally compact group, ({cal B}({L^2}(G))) be the space of all bounded linear operators on L²(G), and (({cal T}({L^2}(G)), ast)) be the Banach algebra of trace class operators on L²(G). In this paper, we focus on some Banach right submodules of ({cal B}({L^2}(G))) over the convolution algebras (({cal T}({L^2}(G)), ast)) and (L¹(G),*). We will see that if the locally compact group G is discrete, then the Banach right ℓ¹(G)-module structures of them are derived from their Banach right ({cal T}({ell ^2}(G)))-module structures. We also study the projectivity of these Banach right ℓ¹(G)-modules.

We propose a unified treatment of extensions of group-valued contents (i.e., additive set functions defined on a ring) by means of adding new null sets. Our approach is based on the notion of a completion ring for a content μ. With every such ring ({cal N}), an extension of μ is naturally associated which is called the ({cal N})-completion of μ. The ({cal N})-completion operation comprises most previously known completion-type procedures and also gives rise to some new extensions, which may be useful for constructing counterexamples in measure theory. We find a condition ensuring that σ-additivity of a content is preserved under the ({cal N})-completion and establish a criterion for the ({cal N})-completion of a measure to be again a measure.

In this note we discuss absolutely norm attaining property (({cal A}{cal N})-property in short) of the Jordan product and Lie-bracket. We propose a functional calculus for positive absolutely norm attaining operators and discuss the stability of the ({cal A}{cal N})-property under the functional calculus. As a consequence we discuss the operator mean of positive ({cal A}{cal N})-operators.

This paper is devoted to the development of Beckenbach’s theory of the meromorphic minimal surfaces. We consider the relationship between the number of separated maximum points of a meromorphic minimal surface and the Baernstein’s T*-function. The results of Edrei, Goldberg, Heins, Ostrovskii, Wiman are generalized. We also give examples showing that the obtained estimates are sharp.

The spaces A ^s_p,q (ℝⁿ)with A ∈ {B, F}, s ∈ ℝ and 0 <p,q ≤ ∞ are usually introduced in terms of Fourier-analytical decompositions. Related characterizations based on atoms and wavelets are known nowadays in a rather final way. Quarks atomize the atoms into constructive building blocks. It is the main aim of this survey to raise quarkonial decompositions to the same level as related representations of the spaces A ^s_p,q (ℝⁿ) in terms of atoms or wavelets culminating finally in universal frame representations of tempered distributions f ∈ S′(ℝⁿ).

In this paper we consider weighted Morrey spaces ({cal M}_{lambda ,{cal F}}^p(w)) adapted to a family of cubes ({cal F}), with the norm

and the question we deal with is whether a Muckenhoupt-type condition characterizes the boundedness of the Hardy–Littlewood maximal operator on ({cal M}_{lambda ,{cal F}}^p(w)).

In the case of the global Morrey spaces (when ({cal F}) is the family of all cubes in ℝⁿ) this question is still open. In the case of the local Morrey spaces (when ({cal F}) is the family of all cubes centered at the origin) this question was answered positively in a recent work of Duoandikoetxea and Rosenthal [2].

We obtain an extension of [2] by showing that the answer is positive when ({cal F}) is the family of all cubes centered at a sequence of points in ℝⁿ satisfying a certain lacunary-type condition.