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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…
Gagliardo-Nirenberg Inequality for rearrangement-invariant Banach function spaces
Alberto Fiorenza, Maria Rosaria Formica, Tomas Roskovec +1
The classical Gagliardo-Nirenberg interpolation inequality is a well-known estimate which gives, in particular, an estimate for the Lebesgue norm of intermediate derivatives of fun…
Detailed proof of classical Gagliardo-Nirenberg interpolation inequality with historical remarks
Alberto Fiorenza, Maria Rosaria Formica, Tomáš Roskovec +1
A carefully written Nirenberg's proof of the well known Gagliardo-Nirenberg interpolation inequality for intermediate derivatives in seems, surprisingly, to be missi…
Exponential tail estimates in the Law of Ordinary Logarithm (LOL) for arrays of random variables
Maria Rosaria Formica, Yurii Vasilovich Kozachenko, Eugeny Ostrovsky +1
We derive exponential bounds for tail of distribution for natural, i.e. under ordinary logarithm, normalized sums of arrays of random variables, not necessarily independent.