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
In this paper, the author studies the mapping properties for some general maximal op- erators and singular integrals on certain function spaces via Fourier transform estimates. Also, some concrete maximal operators an...In this paper, the author studies the mapping properties for some general maximal op- erators and singular integrals on certain function spaces via Fourier transform estimates. Also, some concrete maximal operators and singular integrals are studied as applications.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.
基金Supported by Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.20090003110018)
文摘In this paper, the author studies the mapping properties for some general maximal op- erators and singular integrals on certain function spaces via Fourier transform estimates. Also, some concrete maximal operators and singular integrals are studied as applications.
