Related papers: Discrete Morrey spaces and their generalizations
These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.
The purpose of this paper is to define statistically convergent sequences with respect to the metrics on generalized metric spaces (g-metric spaces) and investigate basic properties of this statistical form of convergence.
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…
In this paper, we establish the compactification of the moduli space in symplectization and and studied the hidden symmetries of its boundary.
We introduce generalized Fofana spaces and we give some of their basic properties. These spaces are a kind of generalization of generalized Morrey spaces. As application, we establish the boundedness of the Hardy-Littlewood maximal operator…
An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…
We study the moduli and determine a homotopy type of the space of all generalized Morse functions on d-manifolds for given d. This moduli space is closely connected to the moduli space of all Morse functions studied in the paper…
In this paper, we present the classification of generalized Wallach spaces and discuss some related problems.
The aim of this text is to extend the theory of generalized ordinary differential equations to the setting of metric spaces. We present existence and uniqueness theorems that significantly improve previous results even when restricted back…
In this paper we examine various properties/constructions which are known for reductive groups and we do some experiments to see to what extent they generalize to symmetric spaces.
This paper includes new bounds concepting the vanishing generalized weighted Morrey space. In this sense, it is outlined improved bounds about the a class of fractional type rough higher order commutators on vanishing generalized weighted…
Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for…
We find a generalization of the Mordell integral and we also establish a set of properties for a generalization of the Mordell integral similar to those in the third author's PhD thesis.
Characterizations of the associated spaces and second associated spaces of the Hardy space on $\mathbb{R}^n$ are given. Some results on the associated spaces of the $\textrm{BMO}(\mathbb{R}^n)$ space are proved also.
We present and prove the version of Marstrand's theorem for discrete metric space. We provide explicit estimates of the quotient of upper and lower densities of measures on this space.
We introduce a general framework allowing to apply the theory of regularity structures to discretisations of stochastic PDEs. The approach pursued in this article is that we do not focus on any one specific discretisation procedure.…
We consider a class of discrete convex functionals which satisfy a (generalized) coarea formula, and study their limit in the continuum.
We define the notion of extrinsic symplectic symmetric spaces and exhibit some of their properties. We construct large families of examples and show how they fit in the perspective of a complete classification of these manifolds. We also…
We define and prove characterizations of Hardy-Orlicz spaces of conformal densities.
In this paper, we give a necessary and sufficient condition that discrete Morse functions on a digraph can be extended to be Morse functions on its transitive closure, from this we can extend the Morse theory to digraphs by using…