2 citations · 2 across the 9 of their papers we have counts for
11 papers
The Trudinger inequality is true for spaces
Ryan Alvarado, Ahmed Dughayshim, Piotr Hajłasz
We prove the Trudinger inequality with exponent for Sobolev spaces on metric measure spaces under the sole measure growth assumption .…
On the measure of the boundary of a Hajłasz-Sobolev -extension domain
Ryan Alvarado, Riddhi Mishra
We prove that the boundary of every bounded -extension domain in a -doubling metric measure space has measure zero whenever , with the additiona…
Real-Variable Theory of Hardy--Lorentz Spaces on Quasi-Ultrametric Spaces of Homogeneous Type with Reverse-Doubling Property
Chenfeng Zhu, Ryan Alvarado, Xianjie Yan +2
Let be an ultra-RD-space with upper dimension ; i.e., it is a quasi-ultrametric space of homogeneous type whose measure satisfies an addition…
Embeddings of variable Sobolev, Besov, and Triebel-Lizorkin spaces on metric measure spaces
Ryan Alvarado, Michał Dymek, Przemysław Górka +1
Sobolev-type embeddings on metric measure spaces encode a subtle interaction between the analytic regularity of functions and the geometry of the underlying domain space. In this p…
On the dimension distortion under fractionally smooth mappings
Ryan Alvarado, Efstathios Konstantinos Chrontsios Garitsis
We determine the extent to which certain classes of fractionally `smooth' continuous mappings between metric spaces distort various dimensions, including the Hausdorff, upper Minko…
A Measure Characterization of Embedding and Extension Domains for Sobolev, Triebel-Lizorkin, and Besov Spaces on Spaces of Homogeneous Type
Ryan Alvarado, Dachun Yang, Wen Yuan
In this article, for an optimal range of the smoothness parameter that depends (quantitatively) on the geometric makeup of the underlying space, the authors identify purely mea…