Weak-type inequalities for higher order Riesz-Laguerre transforms
The aim of this paper is to study the weak type (1,1) boundedness of \(R_{\alpha}^m\), the \(m\)th Riesz-Laguerre transform, with \(m\in Z^d \geq0\), associated with the multidimensional Laguerre operator \(\mathcal L_{\alpha}\), where \(\alpha=(\alpha_1,\dots,\alpha_d)\) is a multi-index with \(\alpha_i\geq0, i=1,\dots,d\). In particular, the authors obtain the boundedness for the Riesz-Laguerre transform of order 2 and also find the sharp polynomial weight \(\omega\) that makes the Riesz-Laguerre transforms of order greater than two continuous from \(L^1(\omega d\mu_{\alpha})\) into \(L^{1,\infty}(d\mu_{\alpha})\), being \(\mu_{\alpha}\) the Laguerre measure.
scientific article; zbMATH DE number 5505680
scientific article