Pertti Mattila
Lipschitz equivalence of subsets of self-conformal sets.
Пт, 09/11/2009 - 19:12 — SomNambulAuthors: Pertti Mattila, Marta Llorente
Subjects: Metric Geometry
AbstractWe give sufficient conditions to guarantee that if two self-conformal sets E
and F have Lipschitz equivalent subsets of positive measure, then there is a
bilipschitz map of E into, or onto, F.Singular integrals on Ahlfors-David regular subsets of the Heisenberg group.
Ср, 09/02/2009 - 12:02 — SomNambulAuthors: Vasilis Chousionis, Pertti Mattila
Subjects: Analysis of PDEs
AbstractWe investigate certain singular integral operators with Riesz-type kernels on
s-dimensional Ahlfors-David regular subsets of Heisenberg groups. We show that
$L^2$-boundedness, and even a little less, implies that $s$ must be an integer
and the set can be approximated at some arbitrary small scales by homogeneous
subgroups. It follows that the operators cannot be bounded on many self similar
fractal subsets of Heisenberg groups.Singular integrals on Ahlfors-David regular subsets of the Heisenberg group.
Ср, 09/02/2009 - 12:02 — SomNambulAuthors: Vasilis Chousionis, Pertti Mattila
Subjects: Analysis of PDEs
AbstractWe investigate certain singular integral operators with Riesz-type kernels on
s-dimensional Ahlfors-David regular subsets of Heisenberg groups. We show that
$L^2$-boundedness, and even a little less, implies that $s$ must be an integer
and the set can be approximated at some arbitrary small scales by homogeneous
subgroups. It follows that the operators cannot be bounded on many self similar
fractal subsets of Heisenberg groups.
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