A new approach to Nikolskii-Besov classes
Vladimir I. Bogachev, Egor D. Kosov, and Svetlana N. Popova
TL;DR
This paper introduces a novel characterization of Nikolskii-Besov classes of fractional smoothness using a nonlinear integration by parts formula, applicable in both finite- and infinite-dimensional Gaussian spaces.
Contribution
It provides a new nonlinear inequality-based characterization of Nikolskii-Besov classes, extending to Gaussian measures in various dimensions.
Findings
New nonlinear inequality characterization of Nikolskii-Besov classes
Extension of characterization to Gaussian measures in finite and infinite dimensions
Potential applications in analysis of fractional smoothness and Gaussian spaces
Abstract
We give a new characterization of Nikolskii-Besov classes of functions of fractional smoothness by means of a nonlinear integration by parts formula in the form of a nonlinear inequality. A similar characterization is obtained for Nikolskii-Besov classes with respect to Gaussian measures on finite- and infinite-dimensional spaces.
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