Let \(\Omega\) be a homogeneous function of degree zero which satisfies \(\Omega \in L^{1}(\mathbb{S}^{n-1})\) and
\(\int_{\mathbb{S}^{n-1}} \Omega(x) \, d\sigma(x) = 0\), and the radial function \(h\) satisfies \((\int_{0}^{\infty} | h(r)| ^{2} \, \frac{dr}{r})^{1/2} \leq 1\). The author proves appropriate \(L^{p}(\mathbb{R}^{n})\) boundedness for a class of maximal operators related to singular integrals with kernels \(\Omega(\frac{y}{| y| })| y| ^{-n}h(| y| )\). This belongs to block spaces and supported by subvarieties. The author also discusses optimal \(L^{2}(\mathbb{R}^{n})\) bounds related to the kernel.