Mixed-norm estimates for a class of nonisotropic directional maximal operators and Hilbert transforms (Q999767)

The main results in this paper extend the known results in the nonisotopic setting of diagonal matrices \(p\) and in fact, hold whenever the eigenvalues of \(p\) have positive real part. For the corresponding Hilbert transform, the author proves an analogous result for all \(d\geq2\) and \(p \in (1,2]\). It is proved as corollaries that \(L^P\)-bounds for variable kernel singular integral operators and Nikodym-type maximal operators taking averages over certain families of curve sets in \(\mathbb R^d\).