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Estimates for tail functions under Riesz transforms in Grand Lebesgue Spaces
Maria Rosaria Formica, Eugene Ostrovsky, Leonid Sirota
We study the tail behaviour of measurable functions under generalized Riesz-type operators in the framework of Grand Lebesgue Spaces. By exploiting the connection between the growt…
Homogeneous kernel integral operators in Grand Lebesgue Spaces
Maria Rosaria Formica, Eugeny Ostrovsky, Leonid Sirota
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.
Norm estimates in Grand Lebesgue Spaces for some operators, including magic square matrices
Maria Rosaria Formica, Eugeny Ostrovsky, Leonid Sirota
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 gener…
Relations between Lorentz-Zygmund and Grand Lebesgue Spaces and norms
Maria Rosaria Formica, Eugeny Ostrovsky, Leonid Sirota
We establish imbedding properties between Grand Lebesgue Spaces and (generalized) Lorentz-Zygmund ones. We extend some known previous results concerning imbedding theorems between…
Generalized Grand Lebesgue Spaces norm estimations for some operators
M. R. Formica, E. Ostrovsky, L. Sirota
We study moment rearrangement invariant spaces, which contain as particular cases the generalized Grand Lebesgue Spaces, and provide norm estimates for some operators, not necessar…
Analog of modulus of convexity for Grand Lebesgue Spaces
M. R. Formica, E. Ostrovsky, L. Sirota
We introduce and evaluate the degree of convexity of an unit ball, so-called, characteristic of convexity (COC) for the Grand Lebesgue Spaces, (GLS), which is a slight analog of th…