The main goal of the paper is to present novel constructions of scales of Banach spaces of Gevrey and more general ultradifferentiable type functions characterized by anisotropic behaviour with respect to bases of constant vector fields X 1,…, Xn .The action under coordinate changes and estimates of compositions in scales of anisotropic Gevrey spaces are derived. As an application we propose generalizations of solvability results for perturbations of powers of multidimensional Mizohata type operators.
Scales of Banach spaces in inhomogeneous Gevrey classes
CADEDDU, LUCIO;GRAMTCHEV, TODOR VASSILEV
2006-01-01
Abstract
The main goal of the paper is to present novel constructions of scales of Banach spaces of Gevrey and more general ultradifferentiable type functions characterized by anisotropic behaviour with respect to bases of constant vector fields X 1,…, Xn .The action under coordinate changes and estimates of compositions in scales of anisotropic Gevrey spaces are derived. As an application we propose generalizations of solvability results for perturbations of powers of multidimensional Mizohata type operators.
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