Singular integrals in the rational Dunkl setting

On $$\mathbb {R}^N$$ equipped with a normalized root system R and a multiplicity function $$k\ge 0$$ let us consider a (not necessarily radial) kernel $$K({\mathbf {x}})$$ satisfying $$|\partial ^\beta K({\mathbf {x}})|\lesssim \Vert {\mathbf {x}}\Vert ^{-{\mathbf {N}}-|\beta |}$$ for $$|\beta |\le s$$ , where $${\mathbf {N}}$$ is the homogeneous dimension of the system $$({\mathbb {R}}^N,R,k)$$ . We additionally assume that $$\begin{aligned} \sup _{0

Keywords:

• Dimension (graph theory)
• algebra
• Combinatorics
• Mathematics
• Kernel (set theory)
• Bounded function
• Homogeneous
• Multiplicity (mathematics)
• Singular integral
• Maximal function

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