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This paper gives a counterexample to show that the first order commutator $\mathcal {C}_2$ 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 $H_{ato,\omega}^{1}(\mathbb{R})$ and study its properties. At last, we prove that $\mathcal {C}_2$ maps $H_{ato,w}^{1}(\mathbb{R})\times H^{1}_{ato,w}(\mathbb{R})$ into $L^{1/2}_{\omega}(\mathbb{R})$.
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참고문헌 (11)
참고문헌 신청
Frédéric Bernicot / 2010 / Use of abstract Hardy spaces, real interpolation and applications to bilinear operators / Mathematische Zeitschrift 265(2):365~400
Frédéric Bernicot / 2008 / New abstract Hardy spaces / Journal of Functional Analysis 255(7):1761~1796
A. P. Calderon / 1965 / COMMUTATORS OF SINGULAR INTEGRAL OPERATORS / Proceedings of the National Academy of Sciences 53(5):1092~1099
Calixto Calderón / 1975 / On commutators of singular integrals / Studia Mathematica 53(2):139~174
R. R. Coifman / 1975 / On Commutators of Singular Integrals and Bilinear Singular Integrals / Transactions of the American Mathematical Society 212:315~331
Frédéric Bernicot / 2008 / New abstract Hardy spaces / Journal of Functional Analysis 255(7):1761~1796
A. P. Calderon / 1965 / COMMUTATORS OF SINGULAR INTEGRAL OPERATORS / Proceedings of the National Academy of Sciences 53(5):1092~1099
Calixto Calderón / 1975 / On commutators of singular integrals / Studia Mathematica 53(2):139~174
R. R. Coifman / 1975 / On Commutators of Singular Integrals and Bilinear Singular Integrals / Transactions of the American Mathematical Society 212:315~331
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