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1. CJM 2013 (vol 66 pp. 429)

Rivera-Noriega, Jorge
 Perturbation and Solvability of Initial $L^p$ Dirichlet Problems for Parabolic Equations over Non-cylindrical Domains For parabolic linear operators $L$ of second order in divergence form, we prove that the solvability of initial $L^p$ Dirichlet problems for the whole range $1\lt p\lt \infty$ is preserved under appropriate small perturbations of the coefficients of the operators involved. We also prove that if the coefficients of $L$ satisfy a suitable controlled oscillation in the form of Carleson measure conditions, then for certain values of $p\gt 1$, the initial $L^p$ Dirichlet problem associated to $Lu=0$ over non-cylindrical domains is solvable. The results are adequate adaptations of the corresponding results for elliptic equations. Keywords:initial $L^p$ Dirichlet problem, second order parabolic equations in divergence form, non-cylindrical domains, reverse HÃ¶lder inequalitiesCategory:35K20

2. CJM 2010 (vol 62 pp. 1276)

El Wassouli, Fouzia
 A Generalized Poisson Transform of an $L^{p}$-Function over the Shilov Boundary of the $n$-Dimensional Lie Ball Let $\mathcal{D}$ be the $n$-dimensional Lie ball and let $\mathbf{B}(S)$ be the space of hyperfunctions on the Shilov boundary $S$ of $\mathcal{D}$. The aim of this paper is to give a necessary and sufficient condition on the generalized Poisson transform $P_{l,\lambda}f$ of an element $f$ in the space $\mathbf{B}(S)$ for $f$ to be in $L^{p}(S)$, $1 > p > \infty.$ Namely, if $F$ is the Poisson transform of some $f\in \mathbf{B}(S)$ (i.e., $F=P_{l,\lambda}f$), then for any $l\in \mathbb{Z}$ and $\lambda\in \mathbb{C}$ such that $\mathcal{R}e[i\lambda] > \frac{n}{2}-1$, we show that $f\in L^{p}(S)$ if and only if $f$ satisfies the growth condition $$\|F\|_{\lambda,p}=\sup_{0\leq r < 1}(1-r^{2})^{\mathcal{R}e[i\lambda]-\frac{n}{2}+l}\Big[\int_{S}|F(ru)|^{p}du \Big]^{\frac{1}{p}} < +\infty.$$ Keywords:Lie ball, Shilov boundary, Fatou's theorem, hyperfuctions, parabolic subgroup, homogeneous line bundleCategories:32A45, 30E20, 33C67, 33C60, 33C55, 32A25, 33C75, 11K70

3. CJM 2009 (vol 62 pp. 202)

Tang, Lin
 Interior $h^1$ Estimates for Parabolic Equations with $\operatorname{LMO}$ Coefficients In this paper we establish \emph{a priori} $h^1$-estimates in a bounded domain for parabolic equations with vanishing $\operatorname{LMO}$ coefficients. Keywords:parabolic operator, Hardy space, parabolic, singular integrals and commutatorsCategories:35K20, 35B65, 35R05

4. CJM 2006 (vol 58 pp. 262)

Biswas, Indranil
 Connections on a Parabolic Principal Bundle Over a Curve The aim here is to define connections on a parabolic principal bundle. Some applications are given. Keywords:parabolic bundle, holomorphic connection, unitary connectionCategories:53C07, 32L05, 14F05

5. CJM 2004 (vol 56 pp. 293)

Khomenko, Oleksandr; Mazorchuk, Volodymyr
 Structure of modules induced from simple modules with minimal annihilator We study the structure of generalized Verma modules over a semi-simple complex finite-dimensional Lie algebra, which are induced from simple modules over a parabolic subalgebra. We consider the case when the annihilator of the starting simple module is a minimal primitive ideal if we restrict this module to the Levi factor of the parabolic subalgebra. We show that these modules correspond to proper standard modules in some parabolic generalization of the Bernstein-Gelfand-Gelfand category $\Oo$ and prove that the blocks of this parabolic category are equivalent to certain blocks of the category of Harish-Chandra bimodules. From this we derive, in particular, an irreducibility criterion for generalized Verma modules. We also compute the composition multiplicities of those simple subquotients, which correspond to the induction from simple modules whose annihilators are minimal primitive ideals. Keywords:parabolic induction, generalized Verma module, simple module, Ha\-rish-\-Chand\-ra bimodule, equivalent categoriesCategories:17B10, 22E47

6. CJM 1997 (vol 49 pp. 798)

Yu, Minqi; Lian, Xiting
 Boundedness of solutions of parabolic equations with anisotropic growth conditions In this paper, we consider the parabolic equation with anisotropic growth conditions, and obtain some criteria on boundedness of solutions, which generalize the corresponding results for the isotropic case. Keywords:Parabolic equation, anisotropic growth conditions, generalized, solution, boundnessCategories:35K57, 35K99.