Related papers: Generalized Grand Lebesgue Spaces norm estimations…

We derive in this preprint the exact up to multiplicative constant non-asymptotical estimates for the norms of some non-linear in general case operators, for example, the so-called maximal functional operators, in two probabilistic…

We extend the classical Lebesgue-Riesz norm estimations for integral operators acting between different classical Lebesgue-Riesz spaces into the Grand Lebesgue Spaces, in the general case. As an example we consider matrix operators acting…

We derive the non-improvable Grand Lebesgue Space norm estimations for multivariate and multidimensional operator of infimal convolution.

In this paper we estimate the norm of operator acting from one Bilateral Grand Lebesgue Space (BGLS) into other Bilateral Grand Lebesgue Space. We also give some examples to show the sharpness of offered inequalities.

We intend to derive the moment and exponential tail estimates for the so-called bivariate or more generally multivariate functional operations, not necessary to be linear or even multilinear. We will show also the strong or at last weak…

In this article we introduce and investigate a new class of rearrangement invariant (r.i.) Banach function spaces, so-called Composed Grand Lebesgue Spaces (CGLS), in particular, Integral Grand Lebesgue Spaces (IGLS), which are some…

We extend the classical Hardy-Sobolev-Poincare-Wirtinger inequalities from the ordinary Lebesgue-Riesz spaces into the Grand Lebesgue ones, with exact constants evaluation.

In this paper we consider composition operator generated by nonsingular measurable transformation between two different Grand Lebesgue Spaces (GLS); we investigate the boundedness, compactness and essential norm of composition operators.

We derive a sharp Grand Lebesgue Space norm estimations for normalized eigen functions for the Laplace-Beltrami operator defined on the compact smooth Riemann manifold. These estimates allow us to deduce in particular the exponential…

We obtain in this short article the non-asymptotic exact estimations for the norm of (generalized) weighted Hardy-Littlewood average integral operator in the so-called Bilateral Grand Lebesgue Spaces. We also give examples to show the…

We give in this short paper a sharp estimate for the norm of a multivariate dilation operator generated by multi-matrix (tensor) linear argument transformation (dilation operator) between two different weight Lebesgue-Riesz and Grand…

We calculate in this paper the norm of composition, multiplicative and product operator, generated by multiplicative and measurable argument transformation between two different ordinary Lebesgue-Riesz and Grand Lebesgue spaces. We set…

We establish imbedding properties between Grand Lebesgue Spaces and (generalized) Lorentz-Zygmund ones. We extend some known previous results concerning imbedding theorems between Grand Lebesgue and classical Lebesgue-Riesz spaces and we…

In this short report we estimate and calculate the exact value of norms of multilinear integral operators having homogeneous kernel, acting between two Grand Lebesgue Spaces.

We obtain in this short article the non-asymptotic estimations for the norm of (generalized) Cesaro-Hardy integral operators in the so-called Bilateral Grand Lebesgue Spaces. We also give examples to show the sharpness of these…

Inequalities for product operators on mixed norm Lebesgue spaces and permuted mixed norm Lebesgue spaces are established. They depend only on inequalities for the factors and on the Lebesgue indices involved. Inequalities for the bivariate…

In this paper we obtain the non - asymptotic estimations for oscillating integral operators in the so - called Bilateral Grand Lebesgue Spaces. We also give examples to show the sharpness of these inequalities.

We provide the conditions for the boundedness of the Bochner-Riesz operator acting between two different Grand Lebesgue Spaces. Moreover we obtain a lower estimate for the constant appearing in the Lebesgue-Riesz norm estimation of the…

We study the problem estimation of classical Lebesgue-Riesz and Grand Lebesgue Norm for the fractional integrals and derivatives for the functions from the classical Lebesgue-Riesz spaces as well as from the modified Besov's spaces.

We generalize in this short paper the classical Luzin's theorem about existence of integral on the measurable function and its multidimensional analogues on the many popular classes of rearrangement invariant (r.i.) spaces, namely, on the…