Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA characterization of BMO self-maps of a metric measure space
114
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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 Gotoh to metric measure spaces. The argument is based on a generalizations Uchiyamas construction of certain extremal BMO-functions and John-Nirenbergs lemma.
rate research
Read More
We study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is a Whitney-type characterization of approximately differentiable functions in this setting. As an application, we prove a Stepanov-type theorem and consider approximate differentiability of Sobolev, BV and maximal functions.
We provide a new geometric proof of Reimanns 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 Heisenberg groups as well as in more general stratified nilpotent Carnot groups.
We prove that every pair of exponential polynomials with imaginary frequencies generates a Poisson-type formula.
We consider some measure-theoretic properties of functions belonging to a Sobolev-type class on metric measure spaces that admit a Poincare inequality and are equipped with a doubling measure. The properties we have selected to study are those that are related to area formulas.
Let $(X,d,mu)$ be a metric measure space satisfying a $Q$-doubling condition, $Q>1$, and an $L^2$-Poincar{e} inequality. Let $mathscr{L}=mathcal{L}+V$ be a Schrodinger operator on $X$, where $mathcal{L}$ is a non-negative operator generalized by a Dirichlet form, and $V$ is a non-negative Muckenhoupt weight that satisfies a reverse Holder condition $RH_q$ for some $qge (Q+1)/2$. We show that a solution to $(mathscr{L}-partial_t^2)u=0$ on $Xtimes mathbb{R}_+$ satisfies the Carleson condition, $$sup_{B(x_B,r_B)}frac{1}{mu(B(x_B,r_B))} int_{0}^{r_B} int_{B(x_B,r_B)} |t abla u(x,t)|^2 frac{mathrm{d}mumathrm{d} t}{t}<infty,$$ if and only if, $u$ can be represented as the Poisson integral of the Schrodinger operator $mathscr{L}$ with trace in the BMO space associated with $mathscr{L}$.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
