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math.FA2014★ 35 cited
An -type estimate for Riesz potentials
Armin Schikorra, Daniel Spector, Jean Van Schaftingen
In this paper we establish new -type estimates for the classical Riesz potentials of order : \[ \|I_αu\|_{L^{N/(N-α)}(\mathbb{R}^N)} \leq C \|Ru\|_{L^1(\mathbb{R}…
math.AP2014★ 217 cited
Groundstates of nonlinear Choquard equations: Hardy-Littlewood-Sobolev critical exponent
Vitaly Moroz, Jean Van Schaftingen
We consider nonlinear Choquard equation $$ - Δu + V u = \bigl(I_α\ast |u|^{\fracα{N}+1}\bigr) |u|^{\fracα{N}-1} u\quad\text{in (\mathbb{R}^N)},$$ where , $V \in L^\infty (…
math.FA2014★ 1 cited
Equivalence between Polyá-Szegő and relative capacity inequalities under rearrangement
Jean Van Schaftingen
The transformations of functions acting on sublevel sets that satisfy a Pólya-Szegő inequality are characterized as those being induced by transformations of sets that do not incre…