The rate of convergence on fractional power dissipative operator on some sobolev type spaces

Abstract

In [3], Chen, Deng, Ding and Fan proved that the fractional power dissipative operator is bounded on Lebesgue spaces Lp(ℝn), Hardy spaces Hp(ℝn) and general mixed norm spaces, which implies almost everywhere convergence of such operator. In this paper, we study the rate of convergence on fractional power dissipative operator on some sobolev type spaces.