대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제56권4호
  • /
  • Pages.885-898
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  • 2019
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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A NOTE ON THE FIRST ORDER COMMUTATOR C2

  • Li, Wenjuan (School of Science Northwest Polytechnical University) ;
  • Liu, Suying (School of Science Northwest Polytechnical University)
  • 투고 : 2018.07.06
  • 심사 : 2018.12.05
  • 발행 : 2019.07.31
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⟨ 이전 논문 다음 논문 ⟩

초록

This paper gives a counterexample to show that the first order commutator $C_2$ is not bounded from $H^1({\mathbb{R}}){\times}H^1({\mathbb{R}})$ into $L^{1/2}({\mathbb{R}})$. Then we introduce the atomic definition of abstract weighted Hardy spaces $H^1_{ato,{\omega}}$$({\mathbb{R}})$ and study its properties. At last, we prove that $C_2$ maps $H^1_{ato,{\omega}}$$({\mathbb{R}}){\times}H^1_{ato,{\omega}}$$({\mathbb{R}})$ into $L^{1/2}_{\omega}$$({\mathbb{R}})$.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China, China Postdoctoral Science Foundation, Central Universities

참고문헌

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