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Let $Omega subset mbr^2$ be an internal chord-arc domain and $varphi : mbs^1 rightarrow partial Omega$ be a homeomorphism. Then there is a diffeomorphic extension $h : mbd rightarrow Omega$ of $varphi .$ We study the relationship between weighted integrability of the derivatives of $h$ and double integrals of $varphi$ and of $varphi^{-1} .$
Let $Omega$ be an internal chord-arc Jordan domain and $varphi:mathbb SrightarrowpartialOmega$ be a homeomorphism. We show that $varphi$ has finite dyadic energy if and only if $varphi$ has a diffeomorphic extension $h: mathbb Drightarrow Omega$ which has finite energy.
Let $mathbb{X}$ be a Jordan domain satisfying hyperbolic growth conditions. Assume that $varphi$ is a homeomorphism from the boundary $partial mathbb{X}$ of $mathbb{X}$ onto the unit circle. Denote by $h$ the harmonic diffeomorphic extension of $varp
In this paper we investigate the regularity properties of weighted Bergman projections for smoothly bounded pseudo-convex domains of finite type in $mathbb{C}^{n}$. The main result is obtained for weights equal to a non negative rational power of the
In this note we show that the weighted $L^{2}$-Sobolev estimates obtained by P. Charpentier, Y. Dupain & M. Mounkaila for the weighted Bergman projection of the Hilbert space $L^{2}left(Omega,dmu_{0}right)$ where $Omega$ is a smoothly bounded pseudoc
We establish a weighted inequality for the Bergman projection with matrix weights for a class of pseudoconvex domains. We extend a result of Aleman-Constantin and obtain the following estimate for the weighted norm of $P$: [|P|_{L^2(Omega,W)}leq C(ma