Weak Type Estimates for Square Functions of Dunkl Heat Flows

Abstract

The weak $(1,1)$ boundedness of the Littlewood--Paley--Stein square function for the Dunkl heat flow is proved via estimates on the Dunkl heat kernel of integral type and the Caldrón--Zygmund decomposition, which is the continuity of the recently work [arXiv:2003.11843] where the dimension-free $L^p$ boundedness of the same square function is studied.

arXiv commentComments are welcome!

References in corpus (5)

• Generalized Hermite Polynomials and the Heat Equation for Dunkl Operators
• A chaotic representation property of the multidimensional Dunkl processes
• Dimension-Free Square Function Estimates for Dunkl Operators
• Sharp Heat Kernel Bounds and Entropy in Metric Measure Spaces
• Littlewood--Paley--Stein Square Functions for the Fractional Discrete Laplacian on $\mathbb{Z}$