Boundedness of commutators of strongly singular convolution operators on Herz-type spaces
Tom 157 / 2003
Studia Mathematica 157 (2003), 33-46
MSC: Primary 42B20.
DOI: 10.4064/sm157-1-3
Streszczenie
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 $b\in {\rm BMO}({{\mathbb R}}^n)$.