2 citations · 3 across the 13 of their papers we have counts for
9 papers · 1 filter
A purely metric characterization of supercritical Sobolev spaces
Ryan Alvarado, Efstathios Konstantinos Chrontsios Garitsis
In this paper we provide a purely metric and derivative-free characterization of continuous mappings in the local supercritical Sobolev space. More specifically, we show that a con…
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…
A simple proof of reflexivity and separability of Sobolev spaces
Ryan Alvarado, Piotr Hajłasz, Lukáš Malý
We present an elementary proof of a well-known theorem of Cheeger which states that if a metric-measure space supports a -Poincaré inequality, then the Sobolev…
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…
Optimal Embeddings for Triebel-Lizorkin and Besov Spaces on Quasi-Metric Measure Spaces
Ryan Alvarado, Dachun Yang, Wen Yuan
In this article, via certain lower bound conditions on the measures under consideration, the authors fully characterize the Sobolev embeddings for the scales of Hajłasz-Triebel-Liz…
Pointwise Characterization of Besov and Triebel-Lizorkin Spaces on Spaces of Homogeneous Type
Ryan Alvarado, Fan Wang, Dachun Yang +1
In this article, the authors establish the pointwise characterization of Besov and Triebel-Lizorkin spaces on spaces of homogeneous type via clarifying the relationship among Hajła…
Sobolev embedding for spaces is equivalent to a lower bound of the measure
Ryan Alvarado, Przemysław Górka, Piotr Hajłasz
It has been known since 1996 that a lower bound for the measure, , implies Sobolev embedding theorems for Sobolev spaces defined on metric-measure spa…
A note on metric-measure spaces supporting Poincaré inequalities
Ryan Alvarado, Piotr Hajłasz
Using a method of Korobenko, Maldonado and Rios we show a new characterization of doubling metric-measure spaces supporting Poincaré inequalities without assuming a priori that the…