Boundedness of singular integrals along surfaces on Lebesgue spaces

In the paper, we establish the Lp(ℝn+1)-boundedness for a class of singular integral operators associated to surfaces of revolution “(y, γ (|y|), y ∈ ℝn” with rough kernels. We also give several applications of this inequality.

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

[2]  James Wright,et al.  Singular Integrals and Maximal Functions Associated to Surfaces of Revolution , 1996 .

[3]  E. Stein.  Singular Integrals and Di?erentiability Properties of Functions , 1971 .

[4]  Lung-kee Chen.  On the maximal Riesz-transforms along surfaces , 1988 .

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

[6]  LP Bounds for Singular Integrals Associated to Surfaces of Revolution , 2002 .

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

[8]  Dachun Yang,et al.  Rough singular integrals associated to surfaces of revolution , 2001 .

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

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

[11]  Elias M. Stein,et al.  Harmonic Analysis (PMS-43), Volume 43: Real-Variable Methods, Orthogonality, and Oscillatory Integrals. (PMS-43) , 1993 .

[12]  Yibiao Pan,et al.  Singular Integrals with Rough Kernels in L log L(Sn−1) , 2002 .

[13]  J. Cooper.  SINGULAR INTEGRALS AND DIFFERENTIABILITY PROPERTIES OF FUNCTIONS , 1973 .

[14]  Timothy S. Murphy,et al.  Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals , 1993 .

[15]  E. Stein,et al.  Problems in harmonic analysis related to curvature , 1978 .