8 citations · 16 across the 10 of their papers we have counts for
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Weak derivatives and metric differentiability almost everywhere
Nikita Evseev
It is known that a Lipschitz continuous map from the Euclidean domain to a metric space is metrically differentiable almost everywhere. When the metric space is a Banach space dual…
Weak differentiability of metric space valued Sobolev maps
Paul Creutz, Nikita Evseev
We show that Sobolev maps with values in a dual Banach space can be characterized in terms of weak derivatives in a weak* sense. Since every metric space embeds isometrically into…
An approach to metric space valued Sobolev maps via weak* derivatives
Paul Creutz, Nikita Evseev
We give a characterization of metric space valued Sobolev maps in terms of weak* derivatives. This corrects a previous result by Hajłasz and Tyson.
Vector-valued Sobolev spaces based on Banach function spaces
Nikita Evseev
It is known that for Banach valued functions there are several approaches to define a Sobolev class. We compare the usual definition via weak derivatives with the Reshetnyak-Sobole…
Sobolev space of functions valued in a monotone Banach family
Nikita Evseev, Alexander Menovschikov
We apply the metrical approach to Sobolev spaces, which arise in various evolution PDEs. Functions from those spaces are defined on an interval and take values in a family of Banac…
Decomposable operators acting between distinct -direct integrals of Banach spaces
Nikita Evseev, Alexander Menovschikov
The notion of decomposable operators acting between distinct -direct integrals of Banach spaces is introduced. We show that these operators generalize the composition operator…
Bounded operators on mixed norm Lebesgue spaces
Nikita Evseev, Alexander Menovschikov
We study two classes of bounded operators on mixed norm Lebesgue spaces, namely composition operators and product operators. A complete description of bounded composition operators…
Bounded composition operator on Lorentz spaces
Nikita Evseev
We study a composition operator on Lorentz spaces. In particular we provide necessary and sufficient conditions under which a measurable mapping induces a bounded composition opera…