Hardy-Littlewood-Paley-type inequalities on compact Lie groups (Q509073)

The classical Hardy-Littlewood inequality on the circle provides a relationship between the \(L^p\) norm of a function \(f\) and its Fourier coefficients \(\hat f(m)\). In this communication, the circle is replaced by a compact Lie group \(G\), and inequalities relating the \(L^p\) norm of \(f\) and its Fourier transform \(\hat f(\xi)\) defined on the dual space \(\hat G\) are stated. As an application, an upper bound for the operator norm \(\|A\|_{L^p(G)\to L^q(G)}\) is given for \(1<p\leq2\leq q<\infty\).