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We establish the equivalence between the Sobolev seminorm‖∇ u‖ L p and a quantity
obtained when replacing strong L p by weak L p in the Gagliardo seminorm| u| W s, p …

The higher order commutators of fractional integral operator I ζ (⋅), V m of variable order is
shown to be bounded from the grand variable Herz spaces K ̇ p (⋅) a (⋅), u, θ (R n) into the …

This paper is essentially a survey on grand and small Lebesgue spaces, which are
rearrangement-invariant Banach function spaces of interest not only from the point of view of …

This work deals with the m th order elliptic equation with non-smooth coefficients in grand-
Sobolev space generated by the norm of the grand-Lebesgue space L q)(Ω), 1< q<+∞ …

Going to Lorentz when fractional Sobolev, Gagliardo and Nirenberg estimates fail |
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Finding a good way to model probability densities is key to probabilistic inference. An ideal
model should be able to concisely approximate any probability while being also compatible …

Despite their pivotal role as primary producers, there is little information as to the diversity
and physiology of cyanobacteria in the meltwater ecosystems of polar regions. Thirty …

In this paper an elliptic operator of the $ m $-th order $ L $ with continuous coefficients in the
$ n $-dimensional domain $\Omega\subset R^{n} $ in the non-standard Grand-Sobolev …

A note on the boundedness of sublinear operators on grand variable Herz spaces | Journal
of Inequalities and Applications Skip to main content SpringerLink Log in Menu Find a …