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In this paper, we give estimates of theL  p   ⁢   (   ℝ  n   )${L^{p}(\mathbb{R}^{n})}$    (1  &lt;  p  &lt;  ∞${1&lt;p&lt;\infty}$   ) and weak type(  1  ,  1  )${(1,1)}$    norm of singular integral operatorT  Ω${T_{\Omega}}$    with homogeneous kernel defined by

Behavior of bounds of singular integrals for large dimension