On a type Sobolev inequality and its applications

Details On a type Sobolev inequality and its applications On a type Sobolev inequality and its applications

2007-01-06

arxiv.org/abs/math/0701191v1

Mathematics

Probability

28 pages

Scientific paper

In the paper we pursue the analysis from the section 5 of the Talagrand's paper "Sample boundedness of stochastic processes under increment conditions." Ann. Probab. 18, No. 1, 1-49. In particular we give the proof of some Sobolev Inequality and then apply it to obtain if and only if condition for all processes with bounded icrements to have bounded samples. The processes are defined on a compact, concave subspaces of $\R^n$ with a metric $d(s,t)=\eta(||s-t||)$, where $\eta$ is concave and $||.||$ is a norm on $\R^n$.

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