Weighted Norm Inequalities on Graphs

作者：Badr Nadine; Maria Martell Jose

来源：Journal of Geometric Analysis, 2012, 22(4): 1173-1210.

DOI：10.1007/s12220-011-9233-9

• Graphs
• Discrete Laplacian
• Riesz transforms
• Square functions
• Muckenhoupt weights
• Spaces of homogeneous type

Let (I%26quot;,mu) 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 a double dagger. We assume that mu is doubling, a uniform lower bound for p(x,y) when p(x,y)%26gt; 0, and gaussian upper estimates for the iterates of p. Under these conditions (and in some cases assuming further some Poincar, inequality) we study the comparability of (I-P)(1/2) f and a double dagger f in Lebesgue spaces with Muckenhoupt weights. Also, we establish weighted norm inequalities for a Littlewood-Paley-Stein square function, its formal adjoint, and commutators of the Riesz transform with bounded mean oscillation functions.

• 出版日期2012-10