论文信息 - Rough singular integrals on Triebel-Lizorkin space and Besov space

Rough singular integrals on Triebel-Lizorkin space and Besov space

Abstract In this paper the authors prove that the homogeneous singular integral T Ω with Ω ∈ H 1 ( S n − 1 ) is bounded on the Triebel–Lizorkin spaces and the Besov spaces. These results answer an open problem proposed by Chen and Zhang in [J. Chen, C. Zhang, Boundedness of rough singular integral on the Triebel–Lizorkin spaces, J. Math. Anal. Appl. 337 (2008) 1048–1052]. The same results hold also for the rough singular integral operators T Ω , h with radial function kernels.

Yong Ding | Yanping Chen | Yong Ding | Yanping Chen

[1] D. Fan,et al. Singular integral operators with rough kernels supported by subvarieties , 1997 .

[2] R. Fefferman,et al. A note on singular integrals , 1979 .

[3] A singular integral operator with rough kernel , 1997 .

[4] L. Grafakos,et al. Convolution Calderón-Zygmund singular integral operators with rough kernels , 1999 .

[5] Charles Fefferman,et al. Some Maximal Inequalities , 1971 .

[6] L. Grafakos. Classical and modern Fourier analysis , 2003 .

[7] A. Zygmund. On Singular Integrals , 1956 .

[8] A. Zygmund,et al. On the existence of certain singular integrals , 1952 .

[9] H. Triebel. Theory Of Function Spaces , 1983 .

[10] Charles Fefferman,et al. A note on spherical summation multipliers , 1973 .

[11] J. Duoandikoetxea,et al. Maximal and singular integral operators via Fourier transform estimates , 1986 .

[12] $L^p$ bounds for singular integrals and maximal singular integrals with rough kernels , 1997, math/9710205.

[13] G. Weiss,et al. Littlewood-Paley Theory and the Study of Function Spaces , 1991 .

[14] B. Jawerth,et al. A discrete transform and decompositions of distribution spaces , 1990 .

[15] Yiming Ying,et al. Singular integral operators on function spaces , 2002 .

[16] Jiecheng Chen,et al. Boundedness of rough singular integral operators on the Triebel–Lizorkin spaces , 2008 .