9 citations · 22 across the 8 of their papers we have counts for
9 papers
On weak associated reflexivity of weighted Sobolev spaces of the first order on real line
V. D. Stepanov, E. P. Ushakova
We study associate and double associate spaces of two-weighted Sobolev spaces of the first order on real half-line and we show that unlike the notion of duality the associativity i…
Norm related inequalities for fractional integrals
Elena P. Ushakova, Kristina E. Ushakova
Fractional spline wavelet systems are considered in the work. Molecular structure of elements of such systems admits estimates connecting norms of fractional integrals' images and…
Images of integration operators in weighted function spaces
Elena P. Ushakova
Images of integration operators of natural orders are considered as elements of Besov and Triebel--Lizorkin spaces with local Muckenhoupt weights on . The results con…
On weighted Hardy inequality with two-dimensional rectangular operator -- extension of the E. Sawyer theorem
V. D. Stepanov, E. P. Ushakova
A characterization is obtained for those pairs of weights and on , for which the two--dimensional rectangular integration operator is bounded from a weighte…
Spline wavelet decomposition in weighted function spaces
Elena P. Ushakova
Battle-Lemarie wavelet systems of natural orders are established in the paper. The main result of the work is decomposition theorem in Besov and Triebel-Lizorkin spaces with local…
Localisation property of Battle-Lemarié wavelets' sums
Elena P. Ushakova, Kristina E. Ushakova
Explicit formulae are given for a type of Battle-Lemarié scaling functions and related wavelets. Compactly supported sums of their translations are established and applied to alter…
Hardy-Steklov operators and embedding inequalities of Sobolev type
Maria G. Nasyrova, Elena P. Ushakova
We characterize a weighted norm inequality which corresponds to the embedding of a class of absolutely continuous functions into the fractional order Sobolev space. The auxiliary r…
On upper estimates for approximation numbers of a Laplace type transformation
Elena P. Ushakova
We deal with a real valued integral operator L of Laplace transformation type acting between Lebesgue spaces on the semi-axis. Sufficient conditions for belonging L to Schatten typ…
On compactness of Laplace and Stieltjes type transformations in Lebesgue spaces
Elena P. Ushakova
We obtain criteria for integral transformations of Laplace and Stieltjes type to be compact on Lebesgue spaces of real functions on the semiaxis.