5 papers
Geometric inequalities related to fractional perimeter: fractional Poincaré, isoperimetric, and boxing inequalities in metric measure spaces
Josh Kline, Panu Lahti, Jiang Li +1
In the setting of a complete, doubling metric measure space supporting a -Poincaré inequality, we show that for all , the following fractional Poincaré ineq…
Trace and Extension Theorems for Besov Functions in Doubling Metric Measure Spaces
Iván Caamaño, Josh Kline
In the setting of a non-complete doubling metric measure space , we construct various bounded linear trace and extension operators for homogeneous and inhomogeneous Besov…
Warped products, solid hyperbolic fillings, and the identity
Ilmari Kangasniemi, Josh Kline, Nageswari Shanmugalingam +1
We construct a large class of metric measure spaces which satisfy the identity , i.e.\ any measurable function …
Self-improvement of fractional Hardy inequalities in metric measure spaces via hyperbolic fillings
Sylvester Eriksson-Bique, Josh Kline
In this paper, we prove a self-improvement result for -fractional Hardy inequalities, in both the exponent and the regularity parameter , for bounded dom…
Characterization of the upper Assouad codimension
Josh Kline, Antti V. Vähäkangas
We present a new notion, the upper Aikawa codimension, and establish its equivalence with the upper Assouad codimension in a metric space with a doubling measure. To achieve this r…