A weighted estimate of the Hörmander multiplier on the Heisenberg group (Q2495288)

A sufficient condition for the weighted boundedness of the Hörmander-type multiplier is found on the Heisenberg group. More exactly, the authors prove that if \(\mathbb{H}^n\) is the \((2n+1)\)-dimensional Heisenberg group, \(\frac{n+1}{2[(n+5)/4]}\leq p\leq 2\) and \(\omega\in A_{\frac{2p[(n+5)/4]}{n+1}}\), or \(2<p\leq (\frac{n+1}{2[(n+5)/4]})'\) and \(\omega^{-1/(p-1)}\in A_{\frac{2p'[(n+5)/4]}{n+1}}\), then the Hörmander multiplier is bounded on \(L^p_\omega(\mathbb{H}^n).\) If \(\omega^{\frac{n+1}{2[(n+5)/4]}}\in A_1,\) then it is of a weighted weak type (1,1). It is a continuation of the article by \textit{C.-C. Lin} [Rev. Mat. Iberoam. 11, No. 2, 269--238 (1995; Zbl 0868.42006)].