Two-parameter Sunouchi operator with respect to character system of p-series field in the Kaczmarz rearrangement

摘要

Let G_p be p-series field. We prove the restricted two-parameter Sunouchi operator T_(χh) is bounded from H~□_q to L_q for 0 < q ≤ 1. By means of interpolation and duality argument, this theorem can be extended to Hardy-Lorentz spaces. As a consequence, we prove the restricted Sunouchi operator is of weak type (L_1,L_1).