In this paper,the authors prove that the commutator [b,T] of the parabolic singular integrals is a compact operator on Lp(Rn)(1 < p < ∞) if and only if b ∈ VMO(Rn,ρ).The result is substantial improvement and extension of some known results.
CHEN YanPing1 & DING Yong2,3 1Department of Mathematics and Mechanics,University of Science and Technology Beijing,Beijing 100083,China
In this paper,we prove that the commutators of maximal hypersingular integrals with rough kernels are bounded from the Sobolev space Lpγ(Rn) to the Lebesgue space Lp(Rn),which is a substantial improvement and an extension of some known results.
In this paper, the author studies the mapping properties for some general maximal operators and singular integrals on certain function spaces via Fourier transform estimates. Also, some concrete maximal operators and singular integrals are studied as applications.
