Weighted Norm Inequalities on Graphs

@inproceedings{BADR2012WeightedNI,
  title={Weighted Norm Inequalities on Graphs},
  author={NADINE BADR and JOS{\'E} MAR{\'I}A MARTELL},
  year={2012}
}
  • NADINE BADR, JOSÉ MARÍA MARTELL
  • Published 2012
Let (Γ, μ) be an infinite graph endowed with a reversible Markov kernel p and let P be the corresponding operator. We also consider the associated discrete gradient ∇. We assume that μ is doubling, a uniform lower bound for p(x, y) when p(x, y) > 0, and gaussian upper estimates for the iterates of p. Under these conditions (and in some cases assuming further some Poincaré inequality) we study the comparability of (I−P )f and ∇f in Lebesgue spaces with Muckenhoupt weights. Also, we establish… CONTINUE READING

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