Lower and upper bounds for the norm of multipliers of multiple trigonometric Fourier series in Lebesgue spaces (Q1580175)

Three theorems are announced without proofs. The first of them is a refinement of Hörmander's multiplier theorem [\textit{L. Hörmander}, Acta Math. 104, 93-140 (1960; Zbl 0093.11402)], which gives an upper bound for the norm of multipliers. The second theorem provides a lower bound in terms of harmonic intervals in \(\mathbb{Z}^n\). The third theorem asserts both lower (in terms of the Shapiro sequence) and upper bounds for the norm of multipliers.