Strong q-variation inequalities for analytic semigroups

Details Strong q-variation inequalities for analytic semigroups Strong q-variation inequalities for analytic semigroups

2011-03-15

arxiv.org/abs/1103.2874v1

Mathematics

Functional Analysis

Scientific paper

Let T : Lp --> Lp be a positive contraction, with p strictly between 1 and infinity. Assume that T is analytic, that is, there exists a constant K such that \norm{T^n-T^{n-1}} < K/n for any positive integer n. Let q strictly betweeen 2 and infinity and let v^q be the space of all complex sequences with a finite strong q-variation. We show that for any x in Lp, the sequence ([T^n(x)](\lambda))_{n\geq 0} belongs to v^q for almost every \lambda, with an estimate \norm{(T^n(x))_{n\geq 0}}_{Lp(v^q)}\leq C\norm{x}_p. If we remove the analyticity assumption, we obtain a similar estimate for the ergodic averages of T instead of the powers of T. We also obtain similar results for strongly continuous semigroups of positive contractions on Lp-spaces.

Affiliated with

Also associated with

No associations

Rating

Strong q-variation inequalities for analytic semigroups 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 Strong q-variation inequalities for analytic semigroups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Strong q-variation inequalities for analytic semigroups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-138656