Singular integrals in the rational Dunkl setting
نویسندگان
چکیده
On $$\mathbb {R}^N$$ equipped with a normalized root system R and multiplicity function $$k\ge 0$$ let us consider (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 $$({\mathbb {R}}^N,R,k)$$ . We additionally assume that $$\begin{aligned} \sup _{0<a<b<\infty }\Big |\int _{a<\Vert {x}}\Vert<b} {x}})\, dw({\mathbf {x}})\Big |<\infty \end{aligned}$$ dw associated measure. prove if s large enough then singular integral Dunkl convolution operator bounded on $$L^p(dw)$$ $$1<p<\infty $$ weak-type (1,1). Furthermore, we study maximal related to convolutions truncation K.
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ژورنال
عنوان ژورنال: Revista Matematica Complutense
سال: 2021
ISSN: ['1696-8220', '1139-1138', '1988-2807']
DOI: https://doi.org/10.1007/s13163-021-00402-1