$L^p$-improving estimates for averages on polynomial curves

Details $L^p$-improving estimates for averages on polynomial curves $L^p$-improving estimates for averages on polynomial curves

2008-12-13

arxiv.org/abs/0812.2589v1

Mathematics

Classical Analysis and ODEs

21 pages

Scientific paper

In the combinatorial method proving of $L^p$-improving estimates for averages along curves pioneered by Christ (IMRN, 1998), it is desirable to estimate the average modulus (with respect to some uniform measure on a set) of a polynomial-like function from below using only the value of the function or its derivatives at some prescribed point. In this paper, it is shown that there is always a relatively large set of points (independent of the particular function to be integrated) for which such estimates are possible. Inequalities of this type are then applied to extend the results of Tao and Wright (JAMS, 2003) to obtain endpoint restricted weak-type estimates for averages over curves given by polynomials.

Affiliated with

Also associated with

No associations

Rating

$L^p$-improving estimates for averages on polynomial curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with $L^p$-improving estimates for averages on polynomial curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and $L^p$-improving estimates for averages on polynomial curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-249941