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

Zongguang Liu

Studia Mathematica (2003)

  • Volume: 157, Issue: 1, page 33-46
  • ISSN: 0039-3223

Abstract

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The author investigates the boundedness of the higher order commutator of strongly singular convolution operator, T b m , on Herz spaces K ̇ q α , p ( ℝ ⁿ ) and K q α , p ( ℝ ⁿ ) , and on a new class of Herz-type Hardy spaces H K ̇ q , b , m α , p , 0 ( ℝ ⁿ ) and H K q , b , m α , p , 0 ( ℝ ⁿ ) , where 0 < p ≤ 1 < q < ∞, α = n(1-1/q) and b ∈ BMO(ℝⁿ).

How to cite

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Zongguang Liu. "Boundedness of commutators of strongly singular convolution operators on Herz-type spaces." Studia Mathematica 157.1 (2003): 33-46. <http://eudml.org/doc/285010>.

@article{ZongguangLiu2003,
abstract = {The author investigates the boundedness of the higher order commutator of strongly singular convolution operator, $T^\{m\}_\{b\}$, on Herz spaces $K̇^\{α,p\}_\{q\}(ℝⁿ)$ and $K^\{α,p\}_\{q\}(ℝⁿ)$, and on a new class of Herz-type Hardy spaces $HK̇^\{α,p,0\}_\{q,b,m\}(ℝⁿ)$ and $HK^\{α,p,0\}_\{q,b,m\}(ℝⁿ)$, where 0 < p ≤ 1 < q < ∞, α = n(1-1/q) and b ∈ BMO(ℝⁿ).},
author = {Zongguang Liu},
journal = {Studia Mathematica},
keywords = {strongly singular convolution operator; BMO; commutator; Herz space; weak Herz space; Hardy space; boundedness},
language = {eng},
number = {1},
pages = {33-46},
title = {Boundedness of commutators of strongly singular convolution operators on Herz-type spaces},
url = {http://eudml.org/doc/285010},
volume = {157},
year = {2003},
}

TY - JOUR
AU - Zongguang Liu
TI - Boundedness of commutators of strongly singular convolution operators on Herz-type spaces
JO - Studia Mathematica
PY - 2003
VL - 157
IS - 1
SP - 33
EP - 46
AB - The author investigates the boundedness of the higher order commutator of strongly singular convolution operator, $T^{m}_{b}$, on Herz spaces $K̇^{α,p}_{q}(ℝⁿ)$ and $K^{α,p}_{q}(ℝⁿ)$, and on a new class of Herz-type Hardy spaces $HK̇^{α,p,0}_{q,b,m}(ℝⁿ)$ and $HK^{α,p,0}_{q,b,m}(ℝⁿ)$, where 0 < p ≤ 1 < q < ∞, α = n(1-1/q) and b ∈ BMO(ℝⁿ).
LA - eng
KW - strongly singular convolution operator; BMO; commutator; Herz space; weak Herz space; Hardy space; boundedness
UR - http://eudml.org/doc/285010
ER -

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