A note on dyadic coverings and nondoubling Calderón-Zygmund theory

Details A note on dyadic coverings and nondoubling Calderón-Zygmund theory A note on dyadic coverings and nondoubling Calderón-Zygmund theory

2012-01-17

arxiv.org/abs/1201.3513v2

Mathematics

Classical Analysis and ODEs

Scientific paper

We construct a family of n+1 dyadic filtrations in R^n, so that every Euclidean ball B is contained in some cube Q of our family satisfying diam(Q) \le c_n diam(B) for some dimensional constant c_n. Our dyadic covering is optimal on the number of filtrations and improves previous results of Christ and Garnett/Jones by extending a construction of Mei for the n-torus. Based on this covering and motivated by applications to matrix-valued functions, we provide a dyadic nondoubling Calder\'on-Zygmund decomposition which avoids Besicovitch type coverings in Tolsa's decomposition. We also use a recent result of Hyt\"onen and Kairema to extend our dyadic nondoubling decomposition to the more general setting of upper doubling metric spaces.

Affiliated with

Also associated with

No associations

Rating

A note on dyadic coverings and nondoubling Calderón-Zygmund theory 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 A note on dyadic coverings and nondoubling Calderón-Zygmund theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A note on dyadic coverings and nondoubling Calderón-Zygmund theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-97608