1 citations · 2 across the 7 of their papers we have counts for
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Quasi Grand Lebesgue Spaces
Maria Rosaria Formica, Eugeny Ostrovsky, Leonid Sirota
We introduce a new class of quasi-Banach spaces as an extension of the classical Grand Lebesgue Spaces for small values of the parameter, and we investigate some its properties, in…
Bochner-Riesz operators in Grand Lebesgue spaces
Maria Rosaria Formica, Eugeny Ostrovsky, Leonid Sirota
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…
Grand Lebesgue Spaces are really Banach algebras relative to the convolution on unimodular locally compact groups
Maria Rosaria Formica, Eugeny Ostrovsky, Leonid Sirota
We prove that the Grand Lebesgue Space, builded on a unimodular locally compact topological group, forms a Banach algebra relative to the convolution.
Criterion for the coincidence of strong and weak Orlicz spaces
Maria Rosaria Formica, Eugeny Ostrovsky
We provide necessary and sufficient conditions for the coincidence, up to equivalence of the norms, between strong and weak Orlicz spaces. Roughly speaking, this coincidence holds…
Fourier Series and Transforms in Grand Lebesgue Spaces As an particular case - exponential Orlicz spaces
E. Ostrovsky, L. Sirota
In this article we investigate the Fourier series and transforms for the functions defined on the [-pi, pi]^ d or on the R^d and belonging to the (Bilateral) Grand Lebesgue Spaces.…