22 citations · 28 across the 7 of their papers we have counts for
7 papers
Exact constant in Sobolev's and Sobolev's trace inequalities for Grand Lebesgue Spaces with monomial weight
E. Ostrovsky, L. Sirota
We generalize in this article the classical Sobolev's and Sobolev's trace inequalities on the Grand Lebesgue Spaces under monomial weight instead the classical Lebesgue or grand Le…
Optimal adaptive multidimensional-time signal energy estimation on the background noise
Eugene Ostrovsky, Eugene Rogover, Leonid Sirota
We construct an adaptive asymptotically optimal in the classical norm of the space L(2,Ω) of square integrable random variables the Energy estimation of a signal (function) observe…
Exact constant in Sobolev's and Sobolev's trace inequalities for Grand Lebesgue Spaces
E. Ostrovsky, E. Rogover, L. Sirota
In this article we generalize the classical Sobolev's and Sobolev's trace inequalities on the Grand Lebesgue Spaces instead the classical Lebesgue Spaces. We will distinguish the c…
Wirtinger-type inequalities for some rearrangement invariant spaces
E. Ostrovsky, E. Rogover, L. Sirota
In this short paper we generalize the classical inequality between the norms in Lebesgue spaces of the functions and its derivatives, which in the multidimensional case are called…
Riesz's and Bessel's Operators in Bilateral Grand Lebesgue Spaces
E. Ostrovsky, E. Rogover, L. Sirota
In this paper we obtain the non - asymptotic estimations for Riesz's and Bessel's potential integral operators in the so - called Bilateral Grand Lebesgue Spaces. We also give exam…
Strichartz type Inequalities for Parabolic and Schrödinger Equations in rearrangement invariant Spaces
E. Ostrovsky, E. Rogover
In this paper we generalize the classical Strichartz estimation for solutions of initial problem for linear parabolic and Schrödinger PDE on many popular classes {\it pairs} of rea…
Maximal Inequalities in Bilateral Grand Lebesque Spaces Over Unbounded Measure
E. Ostrovsky, E. Rogover
In this paper non-asymptotic exact rearrangement invariant norm estimates are derived for the maximum distribution of the family elements of some rearrangement invariant (r.i.) spa…