Whitney coverings and the tent spaces T1,q(γ)T^{1,q}(\gamma) for the Gaussian measure

We introduce a technique for handling Whitney decompositions in Gaussian harmonic analysis and apply it to the study of Gaussian analogues of the classical tent spaces $T^{1,q}$ of Coifman, Meyer and Stein.Comment: 13 pages, 1 figure. Revised version incorporating referee's comments. To appear in Arkiv for Matemati

Close-to-convexity of quasihyperbolic and jj-metric balls

We will consider close-to-convexity of the metric balls defined by the quasihyperbolic metric and the $j$-metric. We will show that the $j$-metric balls with small radii are close-to-convex in general subdomains of \Rn and the quasihyperbolic balls with small radii are close-to-convex in the punctured space.Comment: 12 pages, 2 figure