Boundedness of commutators of strongly singular convolution operators on Herz-type spaces

Zongguang Liu¹

¹ Department of Mathematics China University of Mining and Technology (Beijing) Beijing, 100083 The People's Republic of China

Studia Mathematica, Tome 157 (2003) no. 1, pp. 33-46

Résumé

The author investigates the boundedness of the higher order commutator of strongly singular convolution operator, $T^m_b$, on Herz spaces $\dot {K}^{\alpha ,p}_q({{\mathbb R}}^n)$ and $K^{\alpha ,p}_q({{\mathbb R}}^n)$, and on a new class of Herz-type Hardy spaces $H\dot {K}^{\alpha ,p,0}_{q,b,m}({{\mathbb R}}^n)$ and $HK^{\alpha ,p,0}_{q,b,m}({{\mathbb R}}^n)$, where $0 p\leq 1 q \infty $, $\alpha =n(1-1/q)$ and $b\in {\rm BMO}({{\mathbb R}}^n)$.

Détail

DOI : 10.4064/sm157-1-3

Keywords: author investigates boundedness higher order commutator strongly singular convolution operator herz spaces dot alpha mathbb alpha mathbb class herz type hardy spaces dot alpha mathbb alpha mathbb where leq infty alpha bmo mathbb