5 citations · 11 across the 7 of their papers we have counts for
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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…
Polynomial approximation on convex subsets of $\mathbb R^n
Y. Brudnyi, N. J. Kalton
Let K be a closed bounded convex subset of ; then by a result of the first author, which extends a classical theorem of Whitney there is a constant so that for e…