An application of weighted norm inqualities for maximal functions to semigroups of convolution transforms on $L^{p}_{w}(R^{n})$

Abstract

By applying weighted norm inequalities for maximal functions it is shown that the convolution transforms with kernels \[p(\alpha;t,x)=(2\pi)^{-n}\int_{R^{n}}\exp(ixy-\frac{t}{2}|y|^{\alpha})dy, (t\gt0)\] on $L_{w}^{p}(R^{n})$ to itself form a semigroup of class $(C_{0})$.