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math.FA2011★ 21 cited
Integrals and Potentials of Differential 1-forms on the Sierpinski Gasket
Fabio Cipriani, Daniele Guido, Tommaso Isola +1
We provide a definition of integral, along paths in the Sierpinski gasket K, for differential smooth 1-forms associated to the standard Dirichlet form K. We show how this tool can…
math.FA2007★ 21 cited
Fredholm Modules on P.C.F. Self-Similar Fractals and their Conformal Geometry
Fabio Cipriani, Jean-Luc Sauvageot
The aim of the present work is to show how, using the differential calculus associated to Dirichlet forms, it is possible to construct Fredholm modules on post critically finite fr…
math.FA2007
Hypercontractivity, Nash inequalities, and subordination for classes of nonlinear semigroups
Fabio Cipriani, Gabriele Grillo
A suitable notion of hypercontractivity for a nonlinear semigroup is shown to imply Gagliardo--Nirenberg inequalities for its generator , provided a subhomogeneity pro…