Hölder estimates for subelliptic operators
type: Item
instance of: scholarly article
title: Hölder estimates for subelliptic operators
zbMATH Open document ID: 1028.35051
DOI: 10.1016/S0022-1236(03)00093-4
author: Lihe Wang
published in: Journal of Functional Analysis
publication date: 2003-05-25T00:00:00Z
review text: This paper deals with the equation \(L_\lambda u= u_{xx}+|x|^{2\lambda} u_{yy}= f(x,y)\), \(\lambda> 0\). In the case of \(\lambda\)-integer, \(L_\lambda\) is sum of squares of vector fields operator, and Hörmander has proved subelliptic estimates for it in the scale of Sobolev spaces. The author of the paper under consideration studies optimal Hölder estimates for the same operator. To do this he introduces an appropriate intrinsic Hölder space \(C^\alpha_*\) with the following distance \(d\) between the points \(X= (x_1, y_1)\), \(Y= (x_2,y_2)\): \[ d(X,Y)= (x_1- x_2)+ {|y_1- y_2|\over|x_1|^\lambda+|x_2|^\lambda+|y_1- y_2|^{{\lambda\over 1+\lambda}}}, \] \(\lambda< \alpha< (2\lambda)\wedge 1\) and proves subelliptic type estimates in this scale of spaces.
Mathematics Subject Classification ID: 35H20
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 1915827
zbMATH Keywords: optimal estimates
zbMATH Keywords: intrinsic Hölder space
reviewed by: Peter R. Popivanov
MaRDI profile type: Publication
cites work: Q4365980
cites work: Q3969295
cites work: The Dirichlet problem for the Kohn Laplacian on the Heisenberg group. II
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description: scientific article; zbMATH DE number 1915827