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math.CA2018
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.…
math.CA2017
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…
math.CA2012
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 …
math.CA2012
Optimal relations between Lp-norms for the Hardy operator and its dual
Viktor Kolyada
We obtain sharp two-sided inequalities between norms of functions and , where is the Hardy operator, is its dual, and is a nonnegative…