On a Singular Integral of Christ–Journé Type with Homogeneous Kernel. Issue 1 (1st March 2018) - Ding, Yong; Lai, Xudong
Abstract: In this paper, we prove that the singular integral defined by T_Ω, af(x)=p.v._R^dΩ (x-y)|x-y|^d· m_x, ya· f(y)dy is bounded on L^p(R^d) for 1 < p < ∞ and is of weak type (1, 1), where Ω Llog^+L(S^d-1) and m_x, ya =: _0^1 a(sx + (1 - s)y)ds, with a L^∞ (R^d) satisfying some restricted conditions.