On UC-multipliers for multiple trigonometric systems

Abstract

We investigate the class of sequences w(n) that can serve as almost-everywhere convergence Weyl multipliers for all rearrangements of multiple trigonometric systems. We show that any such sequence must satisfy the bounds log n ≲ w(n) ≲ log² n. Our main result establishes a general equivalence principle between one-dimensional and multidimensional trigonometric systems, which allows one to extend certain estimates known for the one-dimensional case to higher dimensions.