Littlewood–Paley Theory for the Differential Operator
Kwok-Pun Ho
The Education University of Hong Kong, China
![Littlewood–Paley Theory for the Differential Operator $\frac{\partial^2}{\partial x_1^2}\frac{\partial^2}{\partial x_2^2}-\frac{\partial^2}{\partial x_3^2}$ cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-zaa-volume-29-issue-2.png&w=3840&q=90)
Abstract
Littlewood–Paley theory for the differential operator, , is developed. This study leads to the introduction of a new class of Triebel–Lizorkin spaces associated with the dilation , . The corresponding atomic and molecular decompositions are obtained. A frame generated by modulations, dilations and translations is also studied. Using this result, we show that is a linear isomorphism from to .
Cite this article
Kwok-Pun Ho, Littlewood–Paley Theory for the Differential Operator . Z. Anal. Anwend. 29 (2010), no. 2, pp. 183–217
DOI 10.4171/ZAA/1405