45 citations · 146 across the 29 of their papers we have counts for
8 papers · 1 filter
The Strong Maximum Principle for Schrödinger operators on fractals
Marius V. Ionescu, Kasso A. Okoudjou, Luke G. Rogers
We prove a strong maximum principle for Schrödinger operators defined on a class of fractal sets and their blowups without boundary. Our primary interest is in weaker regularity co…
Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities
Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen +3
We introduce heat semigroup-based Besov classes in the general framework of Dirichlet spaces. General properties of those classes are studied and quantitative regularization estima…
BV functions and Besov spaces associated with Dirichlet spaces
Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen +3
We develop a theory of bounded variation functions and Besov spaces in abstract Dirichlet spaces which unifies several known examples and applies to new situations, including fract…
Sobolev Algebra Counterexamples
Thierry Coulhon, Luke G. Rogers
In the Euclidean setting the Sobolev spaces are algebras for the pointwise product when and . This property has recently been extended…
Pseudo-differential Operators on Fractals
Marius Ionescu, Luke G. Rogers, Robert S. Strichartz
We define and study pseudo-differential operators on a class of fractals that include the post-critically finite self-similar sets and Sierpinski carpets. Using the sub-Gaussian es…
Complex Powers of the Laplacian on Affine Nested Fractals as Calderón-Zygmund operators
Marius Ionescu, Luke Rogers
We give the first natural examples of Calderón-Zygmund operators in the theory of analysis on post-critically finite self-similar fractals. This is achieved by showing that the pur…