相关论文: Weak Gurov-Reshetnyak class in metric measure spac…

The optical analogue of quantum weak measurements have shown considerable promise for the amplification and observation of tiny optical beam shifts, namely, the Goos-H\"anchen (GH) and the Imbert-Fedorov (IF) shifts. Here, we demonstrate…

Rational weak mixing is a measure theoretic version of Krickeberg's strong ratio mixing property for infinite measure preserving transformations. It requires "{\tt density}" ratio convergence for every pair of measurable sets in a dense…

Consider the extended hull of a weak model set together with its natural shift action. Equip the extended hull with the Mirsky measure, which is a certain natural pattern frequency measure. It is known that the extended hull is a…

We consider the following class of mixed local-nonlocal equations: \begin{align}\label{abs}\tag{$\mathcal{P}$} -\Delta_p u + (-\Delta)_p^s u = V |u|^{p-2}u \text{ in } \Omega, \end{align} where $s \in (0,1), p \in (1, \infty)$, and the…

We prove that Mal'tsev and Goursat categories may be characterised through stronger variations of the Shifting Lemma, that is classically expressed in terms of three congruences $R$, $S$ and $T$, and characterises congruence modular…

We show that the class $\mathscr{B}$, of discrete groups which satisfy the conclusion of Popa's Cocycle Superrigidity Theorem for Bernoulli actions, is invariant under measure equivalence. We generalize this to the setting of discrete…

We study coercive inequalities on finite dimensional metric spaces with probability measures which do not have volume doubling property. This class of inequalities includes Poincar\'e and Log-Sobolev inequality. Our main result is proof of…

We consider a class of second order degenerate kinetic operators $\mathscr{L}$ in the framework of special relativity. We first describe $\mathscr{L}$ as an H\"ormander operator which is invariant with respect to Lorentz transformations.…

Let $L= -\Delta+ V$ be a Schr\"odinger operator on $\mathbb R^d$, $d\geq 3$, where $V$ is a nonnegative function, $V\ne 0$, and belongs to the reverse H\"older class $RH_{d/2}$. In this paper, we prove a version of the classical theorem of…

We characterize two-weight inequalities for certain maximal truncations of the Hilbert transform in terms of testing conditions on simpler functions. For 1<p<2 and two positive Borel measures u, v on R, we assume that u is doubling, and we…

Let $\mathcal{L}$ be a Schr\"{o}dinger operator and $\mathcal{V}_\varrho(e^{-t\mathcal{L}})$ be the variation operator of heat semigroup associated to $\mathcal{L}$ with $\varrho>2$. In this paper, we first obtain the quantitative weighted…

We investigate characterizations of uniformly rectifiable (UR) metric spaces by so-called weak Carleson conditions for flatness coefficients which measure the extent to which Hausdorff measure on the metric space differs from Hausdorff…

We introduce and study a notion of cylinder coherator similar to the notion of Grothendieck coherator which define more flexible notion of weak infinity groupoids. We show that each such cylinder coherator produces a combinatorial…

In this paper we make a survey of some recent developments of the theory of Sobolev spaces $W^{1,q}(X,\sfd,\mm)$, $1<q<\infty$, in metric measure spaces $(X,\sfd,\mm)$. In the final part of the paper we provide a new proof of the…

We introduce a new higher categorical structure called a weakly globular n-fold category. This structure is based on iterated internal categories and on the notion of weak globularity. We identify a suitable class of pseudo-functors whose…

In this paper, authors prove that if $X$ is a weak Asplund space, then the space $X\times R$ is a weak Asplund space. Thus the author definitely answered an open problem raised by D.G. Larman and R.R. Phelps for 45 years ago (J. London.…

The measure-multiplicity-invariant for masas in $\rm{II}_{1}$ factors was introduced in \cite{MR2261688} to distinguish masas that have the same Puk\'{a}nszky invariant. In this paper we study the measure class in the…

We establish the linear instability of the semiclassical Einstein-Klein-Gordon system linearised about the Minkowski vacuum spacetime. The proof relies on formulating a forcing problem for both metric and state perturbations within the…

Let G be a reductive group (over an algebraically closed field) equipped with the metaplectic data. In this paper we study the corresponding twisted Whittaker category for G. We construct and study a functor from the latter category to the…

In this paper, we deal with weakly coupled elliptic systems $\boldsymbol{\mathcal A}$ with unbounded coefficients. We prove the existence and characterize all the systems of invariant measures for the semigroup $({\bf T}(t))_{t\ge 0}$…