Generalized Littlewood-Paley functions on product spaces
Authors: Al-Qassem, Hussain; Cheng, Leslie; Pan, Yibiao
Source: Turkish Journal of Mathematics,Volume: 45 Issue: 1, Pages: 319-345, DOI: 10.3906/mat-2008-92
Publication Type: Journal Article
Abstract: We are interested in investigating the Lp boundedness of the product of generalized Littlewood-Paley functions SΦ(λ)(f) arising from kernels satisfying only size and cancellation conditions. We obtain Lp estimates of SΦ(λ)(f) for a sharp range of p and under optimal conditions on Φ. Using these estimates and an extrapolation argument, we obtain some new and improved results on generalized Littlewood-Paley functions on product spaces. As a consequence of our main results, we get two results, one of which answers a question posed by D. Fan and H. Wu and the other one answers a question raised by Y. Wu and H. Wu. In addition, one of our lemmas on Triebel-Lizorkin spaces answers a question posed by Y. Wu and H. Wu.