Some new function spaces of variable smoothness
A. I. Tyulenev
TL;DR
This paper introduces new Besov-type function spaces with variable smoothness, providing atomic decompositions via nonlinear spline approximation and characterizing their trace spaces on hyperplanes.
Contribution
It presents novel Besov-type spaces of variable smoothness and offers atomic decomposition and trace space characterization methods.
Findings
Defined new Besov-type spaces with variable smoothness
Provided atomic decomposition using nonlinear spline approximation
Characterized the trace space on hyperplanes
Abstract
The present paper is concerned with new Besov-type space of variable smoothness. Nonlinear spline-approximation approach is used to give atomic decomposition of such space. Characterization of the trace space on hyperplane is also obtained.
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