8 papers
Rearrangement estimates and limiting embeddings for anisotropic Besov spaces
V. I. Kolyada
The paper is dedicated to the study of embeddings of the anisotropic Besov spaces into Lorentz spaces. We find the sharp asymptotic b…
Embedding theorems for Sobolev and Hardy-Sobolev spaces and estimates of Fourier transforms
Viktor Kolyada
We prove embeddings of Sobolev and Hardy-Sobolev spaces into Besov spaces built upon certain mixed norms. This gives an improvment of the known embeddings into usual Besov spaces.…
Fractional integrals and Fourier transforms
Viktor Kolyada
This paper gives a short survey of some basic results related to estimates of fractional integrals and Fourier transforms. It is closely adjoint to our previous survey papers \cite…
Sections of functions and Sobolev type inequalities
V. I. Kolyada
We study functions of two variables whose sections by the lines parallel to the coordinate axis satisfy Lipschitz condition of the order $0<\a\le 1.$ We prove that if for a functio…
On Gagliardo-Nirenberg type inequalities
V. I. Kolyada, F. J. Pérez Lázaro
We present a Gagliardo-Nirenberg inequality which bounds Lorentz norms of the function by Sobolev norms and homogeneous Besov quasinorms with negative smoothness. We prove also oth…
On limiting relations for capacities
V. I. Kolyada
The paper is devoted to the study of limiting behaviour of Besov capacities $\capa (E;B_{p,q}^\a) (0<\a<1)$ of sets in as $\a\to 1$ or $\a\to 0.$ Namely, let …