17 citations · 154 across the 69 of their papers we have counts for
15 papers · 1 filter
The -Besov Capacity Problem
Mario Milman, Jie Xiao
A theory of -Besov capacities is developed and several applications are provided. In particular, we solve an open problem in the theory of limits of the -Besov semi…
Uniqueness of nonnegative weak solution to on
Yuzhao Wang, Jie Xiao
This note shows that under the fractional order differential inequality $$ (\dagger)\quad u^p \le (-Δ)^{\fracα{2}} u\quad\hbox{…
Preduals of quadratic Campanato spaces associated to operators with heat kernel bounds
Liang Song, Jie Xiao, Xuefang Yan
Let be a nonnegative, self-adjoint operator on with the Gaussian upper bound on its heat kernel. As a generalization of the square Campanato space $\mathcal…
Homothetic variant of fractional Sobolev space with application to Navier-Stokes system revisited
Jie Xiao
This note provides a deeper understanding of the main results obtained in the author's 2007 DPDE paper \cite{Xiao}.
Towards spaces of harmonic functions with traces in square Campanato space and its scaling invariant
Renjin Jiang, Jie Xiao, Dachun Yang
For and , let be the space of harmonic functions on the upper half space satisfying $$\displaystyle\sup_{(x_0,r)\in \mathbb…
Geometric Capacity Potentials on Convex Plane Rings
Jie Xiao
Under , this paper presents some old and new convexity/isoperimetry based inequalities for the variational -capacity potentials on convex plane rings.