Related papers: A Bounded mean oscillation (BMO) theorem for small…
This paper deals with a BMO Theorem for $\epsilon$ distorted diffeomorphisms from $\mathbb R^D$ to $\mathbb R^D$ with applications to manifolds of speech and sound. The material for this paper appears in the research memoir [2].
In the two-parameter setting, we say a function belongs to the mean little $BMO$, if its mean over any interval and with respect to any of the two variables has uniformly bounded mean oscillation. This space has been recently introduced by…
We use geometric arguments to prove explicit bounds on the mean oscillation for two important rearrangements on $\mathbb{R}^n$. For the decreasing rearrangement $f^*$ of a rearrangeable function $f$ of bounded mean oscillation (BMO) on…
We consider the problem of distortion minimal morphing of $n$-dimensional compact connected oriented smooth manifolds without boundary embedded in $\R^{n+1}$. Distortion involves bending and stretching. In this paper, minimal distortion…
This paper studies functions of bounded mean oscillation (BMO) on metric spaces equipped with a doubling measure. The main result gives characterizations for mappings that preserve BMO. This extends the corresponding Euclidean results by…
Let $M$ and $N$ be compact smooth oriented Riemannian $n$-manifolds without boundary embedded in $\mathbb{R}^{n+1}$. Several problems about minimal distortion bending and morphing of $M$ to $N$ are posed. Cost functionals that measure…
We introduce another notion of bounded logarithmic mean oscillation in the N-torus and give an equivalent definition in terms of boundedness of multi-parameter paraproducts from the dyadic little BMO of Cotlar-Sadosky to the product BMO of…
We characterize dyadic little BMO via the boundedness of the tensor commutator with a single well chosen dyadic shift. It is shown that several proof strategies work for this problem, both in the unweighted case as well as with Bloom…
We study boundedness properties of a class of multiparameter paraproducts on the dual space of the dyadic Hardy space H_d^1(T^N), the dyadic product BMO space BMO_d(T^N). For this, we introduce a notion of logarithmic mean oscillation on…
In this paper, we characterize Bounded Mean Oscillation (BMO) and establish their connection with Hankel operators on weighted Bergman spaces over tubular domains. By utilizing the space BMO, we provide a new characterization of Bloch…
Random diffeomorphisms with bounded absolutely continuous noise are known to possess a finite number of stationary measures. We discuss dependence of stationary measures on an auxiliary parameter, thus describing bifurcations of families of…
We study solution techniques for elliptic equations in divergence form, where the coefficients are only of bounded mean oscillation (BMO). For $|p-2|<\varepsilon$ and a right hand side in $W^{-1}_p$ we show convergence of a finite element…
We deduce conditional $L_p$-estimates for the variation of a solution of a BSDE. Both quadratic and sub-quadratic types of BSDEs are considered, and using the theory of weighted bounded mean oscillation we deduce new tail estimates for the…
In this paper, we prove that the oscillation operator, variation operator and maximal differential transform associated with the approximate identities are bounded from ${\rm BMO}({\mathbb R}^n)$ to its subspace ${\rm BLO}({\mathbb R}^n)$.
We provide a new geometric proof of Reimann's theorem characterizing quasiconformal mappings as the ones preserving functions of bounded mean oscillation. While our proof is new already in the Euclidean spaces, it is applicable in…
Stroock and Varadhan in 1997 and Geiss in 2005 independently introduced stochastic processes with bounded mean oscillation (BMO) and established their exponential integrability with some unspecified exponential constant. This result is an…
We establish the rectifiability of measures satisfying a linear PDE constraint. The obtained rectifiability dimensions are optimal for many usual PDE operators, including all first-order systems and all second-order scalar operators. In…
We study the action of uncentered fractional maximal functions on mean oscillation spaces associated with the dyadic Hausdorff content $\mathcal{H}_{\infty}^{\beta}$ with $0<\beta\leq n$. For $0 < \alpha < n$, we refine existing results…
We consider a very general definition of BMO on a domain in $\mathbb{R}^n$, where the mean oscillation is taken with respect to a basis of shapes, i.e. a collection of open sets covering the domain. We examine the basic properties and…
In the current paper we obtain discrepancy estimates in exponential Orlicz and BMO spaces in arbitrary dimension $d \ge 3$. In particular, we use dyadic harmonic analysis to prove that for the so-called digital nets of order $2$ the…