Abstract In this paper, we give counterexamples to show that variation and oscillation operators related to rough truncations of the Hilbert transform are not bounded from H1 to L1, and prove variation, oscillation an...Abstract In this paper, we give counterexamples to show that variation and oscillation operators related to rough truncations of the Hilbert transform are not bounded from H1 to L1, and prove variation, oscillation and A-jump operators related to smooth truncations are bounded from H1 to L1.展开更多
基金Supported by NSF of China(Grant Nos.11501169,11371057)
文摘Abstract In this paper, we give counterexamples to show that variation and oscillation operators related to rough truncations of the Hilbert transform are not bounded from H1 to L1, and prove variation, oscillation and A-jump operators related to smooth truncations are bounded from H1 to L1.
