Ioannis Parissis
A Three Dimensional Signed Small Ball Inequality.
Втр, 09/29/2009 - 15:21 — SomNambulAuthors: Ioannis Parissis, Dmitriy Bilyk, Michael T. Lacey, Armen Vagharshakyan
Subjects: Classical Analysis and ODEs
AbstractThe Small Ball Inequality is a conjectural lower bound on sums the L-infinity
norm of sums of Haar functions supported on dyadic rectangles of a fixed volume
in the unit cube. The conjecture is fundamental to questions in discrepancy
theory, approximation theory and probability theory. In this article, we
concentrate on a special case of the conjecture, and give the best known lower
bound in dimension 3, using a conditional expectation argument.A Three Dimensional Signed Small Ball Inequality.
Втр, 09/29/2009 - 15:21 — SomNambulAuthors: Ioannis Parissis, Dmitriy Bilyk, Michael T. Lacey, Armen Vagharshakyan
Subjects: Classical Analysis and ODEs
AbstractThe Small Ball Inequality is a conjectural lower bound on sums the L-infinity
norm of sums of Haar functions supported on dyadic rectangles of a fixed volume
in the unit cube. The conjecture is fundamental to questions in discrepancy
theory, approximation theory and probability theory. In this article, we
concentrate on a special case of the conjecture, and give the best known lower
bound in dimension 3, using a conditional expectation argument.Logarithmic dimension bounds for the maximal function along a polynomial curve.
Пт, 08/28/2009 - 23:56 — SomNambulAuthors: Ioannis Parissis
Subjects: Classical Analysis and ODEs
AbstractLet M denote the maximal function along the polynomial curve
p(t)=(t,t^2,...,t^d) in R^d: M(f)=sup_{r>0} (1/2r) \int_{|t|<r} |f(x-p(t))| dt.
We show that the L^2-norm of this operator grows at most logarithmically with
the parameter d: ||M||_2 < c log d ||f||_2, where c>0 is an absolute constant.
The proof depends on the explicit construction of a "parabolic" semi-group of
operators which is a mixture of stable semi-groups.
Вход в систему
