In this paper, we define and study a canonical Hardy–Littlewood-type maximal operator associated with the one-dimensional generalized Fourier transform. For this operator to which covering methods do not apply, we construct a geometric maximal operator, which controls pointwise the canonical maximal operator, and for which we can use the machinery of real analysis to obtain a maximal theorem.
- Generalized Fourier transform
- Hardy–Littlewood maximal theorem
- Maximal function
ASJC Scopus subject areas
- Geometry and Topology