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1. CJM 2011 (vol 63 pp. 1038)

Cohen, D.; Denham, G.; Falk, M.; Varchenko, A.
 Critical Points and Resonance of Hyperplane Arrangements If $\Phi_\lambda$ is a master function corresponding to a hyperplane arrangement $\mathcal A$ and a collection of weights $\lambda$, we investigate the relationship between the critical set of $\Phi_\lambda$, the variety defined by the vanishing of the one-form $\omega_\lambda=\operatorname{d} \log \Phi_\lambda$, and the resonance of $\lambda$. For arrangements satisfying certain conditions, we show that if $\lambda$ is resonant in dimension $p$, then the critical set of $\Phi_\lambda$ has codimension at most $p$. These include all free arrangements and all rank $3$ arrangements. Keywords:hyperplane arrangement, master function, resonant weights, critical setCategories:32S22, 55N25, 52C35

2. CJM 2007 (vol 59 pp. 276)

Bernardis, A. L.; Martín-Reyes, F. J.; Salvador, P. Ortega
 Weighted Inequalities for Hardy--Steklov Operators We characterize the pairs of weights $(v,w)$ for which the operator $Tf(x)=g(x)\int_{s(x)}^{h(x)}f$ with $s$ and $h$ increasing and continuous functions is of strong type $(p,q)$ or weak type $(p,q)$ with respect to the pair $(v,w)$ in the case $0 Keywords:Hardy--Steklov operator, weights, inequalitiesCategories:26D15, 46E30, 42B25 3. CJM 2006 (vol 58 pp. 492) Chua, Seng-Kee  Extension Theorems on Weighted Sobolev Spaces and Some Applications We extend the extension theorems to weighted Sobolev spaces$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)$domainCategory:46E35 4. CJM 1997 (vol 49 pp. 1010) Lorente, Maria  A characterization of two weight norm inequalities for one-sided operators of fractional type In this paper we give a characterization of the pairs of weights$(\w,v)$such that$T$maps$L^p(v)$into$L^q(\w)$, where$T$is a general one-sided operator that includes as a particular case the Weyl fractional integral. As an application we solve the following problem: given a weight$v$, when is there a nontrivial weight$\w$such that$T$maps$L^p(v)$into$L^q(\w )\$? Keywords:Weyl fractional integral, weightsCategories:26A33, 42B25