相关论文: Atomic decomposition for Morrey-Lorentz spaces
In this paper, we study solutions to the linearized vacuum Einstein equations centered at higher-dimensional Schwarzschild met- rics. We employ Hodge decomposition to split solutions into scalar, co-vector, and two-tensor pieces; the first…
In this paper we prove novel lower bounds for the Ginzburg-Landau energy with or without magnetic field. These bounds rely on an improvement of the "vortex balls construction" estimates by extracting a new positive term in the energy lower…
Let $p(\cdot)$ be a measurable function defined on a probability space satisfying $0<p_-:={\rm ess}\inf_{x\in \Omega}p(x)\leq {\rm ess}\sup_{x\in\Omega}p(x)=:p_+<\infty$. We investigate five types of martingale Hardy spaces $H_{p(\cdot)}$…
In this book, we review various aspects of the Lorentz symmetry breaking, both classical and quantum ones, with the special interest to perturbative generation of Lorentz-breaking terms. We present impacts of Lorentz symmetry breaking in…
Recently representation theory has been used to provide atomic decompositions for a large collection of classical Banach spaces. In this paper we extend the techniques to also include projective representations. As our main application we…
This is the first in a series of papers devoted to the theory of decomposition spaces, a general framework for incidence algebras and M\"obius inversion, where algebraic identities are realised by taking homotopy cardinality of equivalences…
It is known that the necessary and sufficient conditions of the boundedness of commutators on Morrey spaces are given by Di Fazio, Ragusa and Shirai. Moreover, according to the result of Cruz-Uribe and Fiorenza in 2003, it is given that the…
We investigate Hardy spaces $H^1_L(X)$ corresponding to self-adjoint operators $L$. Our main aim is to obtain a description of $H^1_L(X)$ in terms of atomic decompositions similar to such characterisation of the classical Hardy spaces…
We describe the space of isometric immersions from the Lorentz plane $L^2$ into the 3-dimensional anti-de Sitter space, and solve several open problems of this context raised by M. Dajczer and K. Nomizu in 1981. We also obtain from the…
In 1920s R. L. Moore introduced \emph{upper semicontinuous} and \emph{lower semicontinuous} decompositions in studying decomposition spaces. Upper semicontinuous decompositions were studied very well by himself and later by R.H. Bing in…
Explicit separability of general two qubits density matrices is related to Lorentz transformations. We use the 4-dimensional form R(u,v=0,1,2,3) of the Hilbert-Schmidt (HS) decomposition of the density matrix. For the generic case in which…
We introduce the notion of decomposition space as a general framework for incidence algebras and M\"obius inversion: it is a simplicial infinity-groupoid satisfying an exactness condition weaker than the Segal condition, which expresses…
We study a modified Ramsey spectroscopy technique employing slowly decaying states for quantum metrology applications using dense ensembles. While closely positioned atoms exhibit superradiant collective decay and dipole-dipole induced…
The second-order differential equation describes harmonic oscillators, as well as currents in LCR circuits. This allows us to study oscillator systems by constructing electronic circuits. Likewise, one set of closed commutation relations…
In this paper, we investigate necessary and sufficient conditions on the boundedness of composition operators on the Orlicz-Morrey spaces. The results of boundedness include Lebesgue and generalized Morrey spaces as special cases. Further,…
In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of R^n. The main step was a sharp exponential integral inequality for convolutions with the Riesz potential. In this paper we extend and improve Adams' results to…
In this paper, the concept of grand variable Herz-Morrey-Hardy spaces are introduced. We also establish the atomic characterization of these spaces. As an application the authors investigate the continuity of a few singular integral…
Let $\vec{p}\in(0,\,\infty)^n$, $A$ be an expansive dilation on $\mathbb{R}^n$,and $H^{\vec{p}}_A({\mathbb {R}}^n)$ be the anisotropic mixed-norm Hardy space defined via the non-tangential grand maximal function studied by \cite{hlyy20}. In…
For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…
One of the great challenges of modern science is to faithfully model, and understand, matter at a wide range of scales. Starting with atoms, the vastness of the space of possible configurations poses a formidable challenge to any simulation…