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math.CA2022★ 3 cited
Fractional Gagliardo-Nirenberg interpolation inequality and bounded mean oscillation
Jean Van Schaftingen
We prove Gagliardo-Nirenberg interpolation inequalities estimating the Sobolev semi-norm in terms of the bounded mean oscillation semi-norm and a Sobolev semi-norm, with some of th…
math.CA2019★ 2 cited
Range convergence monotonicity for vector measures and range monotonicity of the mass
Justin Dekeyser, Jean Van Schaftingen
We prove that the range of sequence of vector measures converging widely satisfies a weak lower semicontinuity property, that the convergence of the range implies the strict conver…
math.CA2017
Gauge-measurable functions
Augusto C. Ponce, Jean Van Schaftingen
In 1973, E.J. McShane proposed an alternative definition of the Lebesgue integral based on Riemann sums, where gauges are used decide what tagged partitions are allowed. Such an ap…