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An improvement of a lemma of Calderón and Zygmund involving singular spherical harmonic kernels is obtained and a counter-example is given to show that this result is best possible. In a particular case when the singularity is O(|log r|), let $f\in C¹\left({ℝ}^N\setminus 0\right)$ and suppose f vanishes outside of a compact subset of ${ℝ}^N$, N ≥ 2. Also, let k(x) be a Calderón-Zygmund kernel of spherical harmonic type. Suppose f(x) = O(|log r|) as r → 0 in the $L^p$-sense. Set $F\left(x\right)={\int }_{{ℝ}^N}k(x-y)f\left(y\right)dy\forall x\in {ℝ}^N\setminus 0$. Then F(x) = O(log²r) as r → 0 in the $L^p$-sense, 1 < p < ∞....