Exponentially weighted Lp-estimates for ∂¯ on the unit disc

Composition Operators from the Weighted Bergman Space to the nth Weighted Spaces on the Unit Disc

Weighted norm estimates and Lp-spectral independence of linear operators

We investigate the Lp-spectrum of linear operators defined consistently on Lp(Ω) for p0 ≤ p ≤ p1, where (Ω, μ) is an arbitrary σ-finite measure space and 1 ≤ p0 < p1 ≤ ∞. We prove p-independence of the Lp-spectrum assuming weighted norm estimates. The assumptions are formulated in terms of a measurable semi-metric d on (Ω, μ); the balls with respect to this semi-metric are required to satisfy a...

Weighted Lp − Lq estimates of Stokes semigroup in exterior domains

We consider the Navier-Stokes equations in exterior domains and in the weighted L space. For this purpose, we consider the L − L estimates of Stokes semigroup with weight 〈x〉 type. Our proof is based on the cut-off technique with local energy decay estimate proved by Dan, Kobayashi and Shibata [1] and the weighted L − L estimates of Stokes semigroup in the whole space proved by Kobayashi and Ku...

Exponentially Small Estimates for Separatrix Splittings

ABSTRACT This paper reviews our previous estimates and gives an example exhibiting a new phenomenon. In problems involving asymptotics beyond all orders in a perturbation parameter ε, it is a common assumption that the quantity being studied (such as a separatrix splitting distance or angle, a solitary wave mismatch, etc.) can be “estimated” by an expression of the form aεbe−c/ε as ε → 0. Here,...

Gaussian Curvature of the Bergman Metric with Weighted Bergman Kernel on the Unit Disc

In the paper Gaussian curvature of Bergman metric on the unit disc and the dependence of this curvature on the weight function has been studied.