1. CJM Online first
 Wang, Xing; Zhang, Chunjie

Pointwise convergence of solutions to the SchrÃ¶dinger equation on manifolds
Let $(M^n,g)$ be a Riemannian manifold without
boundary. We study the amount of initial regularity is required
so that the solution to free SchrÃ¶dinger equation converges
pointwise to its initial data. Assume the initial data is in
$H^\alpha(M)$. For Hyperbolic Space, standard Sphere and the
2 dimensional Torus, we prove that $\alpha\gt \frac{1}{2}$ is enough.
For general compact manifolds, due to lacking of local smoothing
effect, it is hard to beat the bound $\alpha\gt 1$ from interpolation.
We managed to go below 1 for dimension $\leq 3$. The more interesting
thing is that, for 1 dimensional compact manifold, $\alpha\gt \frac{1}{3}$
is sufficient.
Keywords:pointwise convergence, SchrÃ¶dinger operator, manifold, Strichartz estimate Categories:35L05, 46E35, 42B37 

2. CJM 2013 (vol 66 pp. 721)
 DurandCartagena, E.; Ihnatsyeva, L.; Korte, R.; Szumańska, M.

On Whitneytype Characterization of Approximate Differentiability on Metric Measure Spaces
We study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is a Whitneytype characterization of approximately differentiable functions in this setting.
As an application, we prove a Stepanovtype theorem and consider approximate differentiability of Sobolev, $BV$ and maximal functions.
Keywords:approximate differentiability, metric space, strong measurable differentiable structure, Whitney theorem Categories:26B05, 28A15, 28A75, 46E35 

3. CJM 2013 (vol 66 pp. 641)
 Grigor'yan, Alexander; Hu, Jiaxin

Heat Kernels and Green Functions on Metric Measure Spaces
We prove that, in a setting of local Dirichlet forms on metric measure
spaces, a twosided subGaussian estimate of the heat kernel is equivalent
to the conjunction of the volume doubling propety, the elliptic Harnack
inequality and a certain estimate of the capacity between concentric balls.
The main technical tool is the equivalence between the capacity estimate and
the estimate of a mean exit time in a ball, that uses twosided estimates of
a Green function in a ball.
Keywords:Dirichlet form, heat kernel, Green function, capacity Categories:35K08, 28A80, 31B05, 35J08, 46E35, 47D07 

4. CJM 2007 (vol 59 pp. 1135)
 Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari

Sobolev Extensions of HÃ¶lder Continuous and Characteristic Functions on Metric Spaces
We study when characteristic and H\"older continuous functions
are traces of Sobolev functions on doubling metric measure spaces.
We provide analytic and geometric conditions sufficient for extending
characteristic and H\"older continuous functions into globally defined
Sobolev functions.
Keywords:characteristic function, Newtonian function, metric space, resolutivity, HÃ¶lder continuous, Perron solution, $p$harmonic, Sobolev extension, Whitney covering Categories:46E35, 31C45 

5. CJM 2006 (vol 58 pp. 492)
 Chua, SengKee

Extension Theorems on Weighted Sobolev Spaces and Some Applications
We extend the extension theorems to weighted Sobolev spaces
$L^p_{w,k}(\mathcal D)$ on $(\varepsilon,\delta)$ domains with doubling weight $w$
that satisfies a Poincar\'e inequality and such that $w^{1/p}$ is locally
$L^{p'}$. We also make use of the main theorem to improve weighted
Sobolev interpolation inequalities.
Keywords:PoincarÃ© inequalities, $A_p$ weights, doubling weights, $(\ep,\delta)$ domain, $(\ep,\infty)$ domain Category:46E35 

6. CJM 2002 (vol 54 pp. 1280)
 Skrzypczak, Leszek

Besov Spaces and Hausdorff Dimension For Some CarnotCarathÃ©odory Metric Spaces
We regard a system of left invariant vector fields $\mathcal{X}=\{X_1,\dots,X_k\}$
satisfying the H\"ormander condition and the related CarnotCarath\'eodory metric on a
unimodular Lie group $G$. We define Besov spaces corresponding to the subLaplacian
$\Delta=\sum X_i^2$ both with positive and negative smoothness. The atomic
decomposition of the spaces is given. In consequence we get the distributional
characterization of the Hausdorff dimension of Borel subsets with the Haar measure
zero.
Keywords:Besov spaces, subelliptic operators, CarnotCarathÃ©odory metric, Hausdorff dimension Categories:46E35, 43A15, 28A78 
