Weighted Norm Inequalities on Graphs |
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Authors: | Nadine Badr José María Martell |
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Affiliation: | 1. Institut Camille Jordan, Universit?? de Lyon et CNRS, 43, boulevard du 11 novembre 1918, 69622, Villeurbanne Cedex, France 2. Instituto de Ciencias Matem??ticas CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones Cient??ficas, C/ Nicol??s Cabrera, 13-15, 28049, Madrid, Spain
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Abstract: | Let (??,??) 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 ?? 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)1/2 f and ?f in Lebesgue spaces with Muckenhoupt weights. Also, we establish weighted norm inequalities for a Littlewood?CPaley?CStein square function, its formal adjoint, and commutators of the Riesz transform with bounded mean oscillation functions. |
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