4 papers
Fractional Leibniz rules for the Dunkl Laplacian in Besov and Triebel--Lizorkin spaces
The Anh Bui, Xueting Han, Suman Mukherjee
Let be the Dunkl Laplacian on the Euclidean space associated with a normalized root system and a multiplicity function , . We establish…
Weighted variational inequalities for the fractional Dunkl heat semigroup
Suman Mukherjee
We investigate the convergence properties of the family of operators $$ \mathcal{T}_{\bf N} f(x)=\sum_{j=N_1}^{N_2} v_j\Bigl( e^{-a_{j+1}(-Î_k)^s}f(x) - e^{-a_j(-Î_k)^s}f(x) \Big…
Large time behaviour of the fractional heat equation associated with the Dunkl Laplacian
Suman Mukherjee
We consider the fractional heat equation associated with the Dunkl Laplacian and prove that the weak solutions to this equation converge to the fundamental solution as time becomes…
On the boundedness of Dunkl multipliers
Suman Mukherjee, Sundaram Thangavelu
In this article we use Littlewood-Paley-Stein theory to prove two versions of Dunkl multiplier theorem when the multiplier satisfies a modified Hörmander condition. When $ m…