A weighted Riesz–Kolmogorov criterion and multilinear extrapolation of compactness on variable Lebesgue spaces

by Dr Stefanos Lappas (Mathematical Institute, University of Bonn)

Friday Nov 6, 2026, 2:15 PM → 3:15 PM Europe/Berlin

Endenicher Allee 60, Seminarraum 0.011 (Mathezentrum)

We present a weighted Riesz–Kolmogorov criterion for relatively compact sets in variable Lebesgue spaces $L^{p(\cdot)}(w)$. Using this criterion, we prove a multilinear extrapolation principle for compactness. More precisely, we show that if an $m$-linear operator is bounded on weighted variable Lebesgue spaces for all multilinear variable Muckenhoupt weights and compact for a single choice of exponents and weights, then it is compact for all admissible variable exponents and weights. As applications, we obtain new compactness results for commutators of multilinear $\omega$-Calderón–Zygmund operators, multilinear fractional integrals and multilinear Fourier multipliers. This talk is based on joint work with S. Kakaroumpas.