Littlewood-Paley functionals on graphs

Abstract

Let $\Gamma$ be a graph equipped with a Markov operator $P$. We introduce discrete fractional Littlewood-Paley square functionals and prove their $L^p$-boundedness under various geometric assumptions on $\Gamma$.

2nd version. 30 pages. Minor changes asking by the reviewer. In particular, a clarification on the proof of Proposition C.2. Appears in Mathematical News / Mathematische Nachrichten, Wiley-VCH Verlag, 2015, http://onlinelibrary.wiley.com/doi/10.1002/mana.201400119/abstract