5 citations · 11 across the 7 of their papers we have counts for
7 papers
Multivariate Bounded Variation Functions of Jordan-Wiener Type
A. Brudnyi, Yu. Brudnyi
We introduce and study spaces of multivariate functions of bounded variation generalizing the classical Jordan and Wiener spaces. Multivariate generalizations of the Jordan space w…
On Banach Structure of Multivariate BV Spaces I
Alexander Brudnyi, Yuri Brudnyi
We introduce and study multivariate generalizations of the classical BV spaces of Jordan, F. Riesz and Wiener. The family of the introduced spaces contains or is intimately related…
Remez Type Inequalities and Morrey-Campanato Spaces on Ahlfors Regular Sets
A. Brudnyi, Yu. Brudnyi
The paper presents several new results on Remez type inequalities for real and complex polynomials in n variables on Ahlfors regular subsets of Lebesgue n-measure zero. As an appli…
Extension of Lipschitz Functions Defined on Metric Subspaces of Homogeneous Type
A. Brudnyi, Yu. Brudnyi
If a metric subspace of an arbitrary metric space carries a doubling measure , then there is a simultaneous linear extension of all Lipschitz functions on ra…
A Universal Lipschitz Extension Property of Gromov Hyperbolic Spaces
A. Brudnyi, Yu. Brudnyi
A metric space has the universal Lipschitz extension property if for each subspace S embedded quasi-isometrically into an arbitrary metric space M there exists a continuous linear…
Metric Spaces with Linear Extensions Preserving Lipschitz Condition
A. Brudnyi, Yu. Brudnyi
We study a new bi-Lipschitz invariant λ(M) of a metric space M; its finiteness means that Lipschitz functions on an arbitrary subset of M can be linearly extended to functions on M…