Hörmander Fourier multiplier theorems with optimal regularity in bi-parameter Besov spaces (Q2053655)

The paper under review is concerned with Fourier multipliers satisfying smoothness assumptions in bi-parameter Besov spaces. Main results are bi-parameter analogues of Hörmander-type multiplier theorems on Lebesgue spaces \(L^p(\mathbb{R}^{n_1} \times \mathbb{R}^{n_2})\) for \(1<p< \infty\) and on product Hardy spaces \(H^p(\mathbb{R}^{n_1} \times \mathbb{R}^{n_2})\) for \(0<p\leq 1\). These results improve earlier results for multipliers in bi-parameter Sobolev spaces. The sharpness of their bi-parameter Besov space assumptions is also obtained in the paper.