Boundedness of rough integral operators on Triebel-Lizorkin spaces

We prove the boundedness of several classes of rough integral operators on Triebel-Lizorkin spaces. Our results represent improvements as well as natural extensions of many previously known results.

[1]  Lu Shanzhen,et al.  Criterion on Lp-boundedness for a class of oscillatory singular integrals with rough kernels , 1992 .

[2]  Singular integrals with mixed homogeneity in Triebel–Lizorkin spaces , 2008 .

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

[4]  K. Guo,et al.  A Note of a Rough Singular Integral Operator , 1999 .

[5]  A class of oscillatory singular integrals on triebel-lizorkin spaces , 2006 .

[6]  A. Seeger.  Singular integral operators with rough convolution kernels , 1996 .

[7]  Chunjie Zhang.  WEIGHTED ESTIMATES FOR CERTAIN ROUGH SINGULAR INTEGRALS , 2008 .

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

[9]  Elias M. Stein,et al.  On the functions of Littlewood-Paley, Lusin, and Marcinkiewicz , 1958 .

[10]  Jiecheng Chen,et al.  A Note on a Marcinkiewicz Integral Operator , 2001 .

[11]  Jiecheng Chen,et al.  Boundedness of rough oscillatory singular integral on Triebel-Lizorkin spaces , 2005 .

[12]  Yong Ding,et al.  Rough singular integrals on Triebel-Lizorkin space and Besov space , 2008 .

[13]  On the boundedness of rough oscillatory singular integrals on Triebel-Lizorkin spaces , 2011 .

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

[15]  E. Stein,et al.  Harmonic analysis on nilpotent groups and singular integrals , 1988 .

[16]  Ahmad Al-Salman,et al.  Singular Integrals With Rough Kernels , 2004, Canadian Mathematical Bulletin.

[17]  Sharp Lorentz space estimates for rough operators , 1999, math/9912098.

[18]  E. Stein.  ON THE FUNCTIONS OF LITTLEWOOD-PALEY, , 2010 .

[19]  G. Weiss,et al.  Extensions of Hardy spaces and their use in analysis , 1977 .

[20]  Shan-zhen Lu,et al.  Oscillatory Singular Integrals with Rough Kernel , 1995 .

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

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

[23]  E. Stein,et al.  Harmonic analysis on nilpotent groups and singular integrals I. Oscillatory integrals , 1987 .

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